InternLM/InternBootcamp
1
0
Fork 0
mirror of https://github.com/InternLM/InternBootcamp.git synced 2026-04-19 12:58:04 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions
InternBootcamp/examples/data/Intenbootcamp_eval/korOperationUnicode25b3.jsonl
Yongkang Chen a8249acc18
update to tech report version (#10) 
* feat(run_eval): add checkpoint resume functionality and update example documentation;
- update new bootcamp benchmark dataset

* refactor(data_pipeline): optimize data generation pipeline; add multiple preset configurations for data generation

* docs: update bootcamp list and add new scripts

- Update Fulllist_InternBootcamp.md with new bootcamps and categories
- Add new scripts to .gitignore:
  - examples/pipelines/filter_autogen_configs.py
  - examples/pipelines/quickgen_data_configs_from_eval_meta.py
- Update dependencies in setup.py:
  - Add scipy and scikit-learn

* refactor(internbootcamp): update bootcamp modules and improve error handling

- Update import statements in __init__.py files
- Add timestamp to target directory name in verl_data_preprocess.py
- Improve error handling and scoring logic in bootcamp_judger.py
- Remove unnecessary comments and update puzzle descriptions in multiple files
2025-08-28 12:39:47 +08:00

100 lines
54 KiB
JSON
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x^{5}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{5}", "x_value": null, "correct_answer": "5 x^{4} \\cos{\\left(x^{5} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(x^{2} \\left(x \\cos{\\left(x \\right)} + 2 \\sin{\\left(x \\right)}\\right) \\sin{\\left(x \\right)} \\cos{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} + x \\sin{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)} + 2 \\sin{\\left(x \\right)} \\sin{\\left(x^{2} \\sin{\\left(x \\right)} \\right)}\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = x. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "x", "x_value": null, "correct_answer": "x \\left(2 \\log{\\left(x \\right)} + 1\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\sin{\\left(x \\right)}, g(x) = \\log{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Provide an integer within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\sin{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "x_value": "1", "correct_answer": "0", "answer_format": "integer"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\cos{\\left(x \\right)}, g(x) = x^{2}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\cos{\\left(x \\right)}", "g": "x^{2}", "x_value": null, "correct_answer": "2 x^{3} \\left(- x^{2} \\sin{\\left(x^{2} \\right)} + 2 \\cos{\\left(x^{2} \\right)}\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{2} e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{2} e^{x}", "x_value": null, "correct_answer": "- x \\left(x + 2\\right) e^{x} \\sin{\\left(x^{2} e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2}, g(x) = x \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2}", "g": "x \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "2 x \\left(\\log{\\left(x \\right)} + 1\\right) \\log{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = x \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "x \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "3 x^{2} \\left(\\log{\\left(x \\right)} + 1\\right) \\log{\\left(x \\right)}^{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = x^{2} \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{2}{x} + \\frac{1}{x \\log{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "e^{\\sin{\\left(x \\right)}} \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(x \\log{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)} + x \\cos{\\left(x \\right)} + 2 \\log{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} \\sin{\\left(x \\right)} + 2 \\sin{\\left(x \\right)}\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{2} e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{2} e^{x}", "x_value": null, "correct_answer": "- x \\left(x + 2\\right) e^{x} \\sin{\\left(x^{2} e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} e^{x}, g(x) = x^{\\frac{3}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} e^{x}", "g": "x^{\\frac{3}{2}}", "x_value": null, "correct_answer": "\\frac{3 \\left(x^{\\frac{7}{2}} + 2 x^{2}\\right) e^{x^{\\frac{3}{2}}}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2}, g(x) = x^{2} \\log{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Provide an integer within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": "1", "correct_answer": "0", "answer_format": "integer"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = x^{\\frac{5}{2}}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Write fractions as 'a/b' within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "x^{\\frac{5}{2}}", "x_value": "1", "correct_answer": "15/2", "answer_format": "fraction"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x^{\\frac{3}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{\\frac{3}{2}}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{x} \\cos{\\left(x^{\\frac{3}{2}} \\right)}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = x^{2} \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "3 x^{5} \\left(- x \\sin{\\left(x \\right)} + 2 \\cos{\\left(x \\right)}\\right) \\cos^{2}{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\left(\\log{\\left(x \\right)} + 1\\right) \\cos{\\left(x \\log{\\left(x \\right)} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = \\sqrt{x}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "\\sqrt{x}", "x_value": "1", "correct_answer": "1.36", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = x \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\tan{\\left(x \\right)} + \\frac{1}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{5}{2}}, g(x) = x. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{5}{2}}", "g": "x", "x_value": null, "correct_answer": "\\frac{5 x^{\\frac{3}{2}}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- e^{\\cos{\\left(x \\right)}} \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = \\log{\\left(x \\right)}. Find f△g at x = 2.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 2.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "x_value": "2", "correct_answer": "0.09", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\cos{\\left(x \\right)}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\cos{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "\\left(\\sin{\\left(\\cos{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)} - 2 \\cos{\\left(\\cos{\\left(x \\right)} \\right)}\\right) \\sin{\\left(x \\right)} \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = \\sqrt{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "\\sqrt{x}", "x_value": null, "correct_answer": "\\frac{\\log{\\left(x \\right)} + 2}{4 \\sqrt{x}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2}, g(x) = x^{2} \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "2 x^{3} \\left(2 \\log{\\left(x \\right)} + 1\\right) \\log{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\left(\\log{\\left(x \\right)} + 1\\right) \\cos{\\left(x \\log{\\left(x \\right)} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{\\sin{\\left(x \\right)}} \\cos{\\left(x \\right)}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- 3 \\sin{\\left(x \\right)} \\cos^{2}{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\cos{\\left(x \\right)}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\cos{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\left(- \\sin{\\left(x \\right)} \\sin{\\left(\\sin{\\left(x \\right)} \\right)} + \\cos{\\left(\\sin{\\left(x \\right)} \\right)}\\right) \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{2} \\cos{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": "1", "correct_answer": "-0.12", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{\\log{\\left(\\log{\\left(x \\right)} \\right)} + 1}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sqrt{x}, g(x) = x e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x e^{x}", "x_value": null, "correct_answer": "\\frac{\\sqrt{x e^{x}} \\left(x + 1\\right)}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\tan{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x e^{x}", "x_value": null, "correct_answer": "\\left(x \\log{\\left(x e^{x} \\right)} + x + \\log{\\left(x e^{x} \\right)} + 1\\right) e^{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x^{3} \\left(x \\sin{\\left(2 x \\right)} - 2 \\cos{\\left(2 x \\right)} + 2\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = x. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "x", "x_value": null, "correct_answer": "x \\cos{\\left(x \\right)} + \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\sin{\\left(2 x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\sin{\\left(2 x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x e^{x}, g(x) = x^{\\frac{5}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x e^{x}", "g": "x^{\\frac{5}{2}}", "x_value": null, "correct_answer": "\\frac{5 \\left(x^{\\frac{3}{2}} + x^{4}\\right) e^{x^{\\frac{5}{2}}}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{\\frac{5}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{\\frac{5}{2}}", "x_value": null, "correct_answer": "- \\frac{5 x^{\\frac{3}{2}} \\sin{\\left(x^{\\frac{5}{2}} \\right)}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{1}{x \\log{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\log{\\left(x \\right)}, g(x) = x \\log{\\left(x \\right)}. Find f△g at x = 2.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 2.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x \\log{\\left(x \\right)}", "x_value": "2", "correct_answer": "1.22", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{\\frac{3}{2}}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{\\frac{3}{2}}", "x_value": "1", "correct_answer": "-1.26", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x e^{x}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x e^{x}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\left(\\cos{\\left(x \\right)} + 1\\right) e^{\\cos{\\left(x \\right)}} \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{5}{2}}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{5}{2}}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{5 \\log{\\left(x \\right)}^{\\frac{3}{2}}}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{7}, g(x) = x^{7}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{7}", "g": "x^{7}", "x_value": null, "correct_answer": "49 x^{48}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sqrt{x}, g(x) = x^{4}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x^{4}", "x_value": null, "correct_answer": "\\frac{2 \\sqrt{x^{4}}}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = \\cos{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "x_value": "1", "correct_answer": "-0.72", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{\\frac{5}{2}}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{\\frac{5}{2}}", "x_value": "1", "correct_answer": "-2.10", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = x^{2} e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "x^{2} e^{x}", "x_value": null, "correct_answer": "x \\left(x^{2} \\left(x + 2\\right) e^{x} \\cos{\\left(x^{2} e^{x} \\right)} + x \\sin{\\left(x^{2} e^{x} \\right)} + 2 \\sin{\\left(x^{2} e^{x} \\right)}\\right) e^{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\frac{3 \\sin{\\left(x \\right)} \\sqrt{\\cos{\\left(x \\right)}}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = x^{\\frac{3}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "x^{\\frac{3}{2}}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{x} e^{x^{\\frac{3}{2}}}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = x^{2}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "x^{2}", "x_value": null, "correct_answer": "2 x \\left(x^{2} \\cos{\\left(x^{2} \\right)} + \\sin{\\left(x^{2} \\right)}\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x e^{x}", "x_value": null, "correct_answer": "\\left(x + 1\\right) e^{x} \\cos{\\left(x e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{5}{2}}, g(x) = x \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{5}{2}}", "g": "x \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{5 \\left(x \\sin{\\left(x \\right)}\\right)^{\\frac{5}{2}} \\left(\\frac{x}{\\tan{\\left(x \\right)}} + 1\\right)}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "e^{x}", "x_value": null, "correct_answer": "\\left(\\log{\\left(e^{x} \\right)} + 1\\right) e^{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = x^{2} e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "x^{2} e^{x}", "x_value": null, "correct_answer": "x^{3} \\left(2 x \\log{\\left(x^{2} e^{x} \\right)} + x + 4 \\log{\\left(x^{2} e^{x} \\right)} + 2\\right) e^{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x e^{x}", "x_value": null, "correct_answer": "\\left(x + 1\\right) e^{x} \\cos{\\left(x e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} e^{x}, g(x) = x^{2} \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} e^{x}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "x^{3} \\left(x^{2} \\left(- \\frac{x \\sin{\\left(2 x \\right)}}{2} + \\cos{\\left(2 x \\right)} + 1\\right) - 2 x \\sin{\\left(x \\right)} + 4 \\cos{\\left(x \\right)}\\right) e^{x^{2} \\cos{\\left(x \\right)}} \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x^{4}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x^{4}", "x_value": null, "correct_answer": "4 x^{3} \\left(\\log{\\left(x^{4} \\right)} + 1\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sqrt{x}, g(x) = x^{3}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x^{3}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{x^{3}}}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\frac{3 \\sin{\\left(x \\right)} \\sqrt{\\cos{\\left(x \\right)}}}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x^{2} \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(2 \\log{\\left(x \\right)} + 1\\right) \\cos{\\left(x^{2} \\log{\\left(x \\right)} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\cos{\\left(x \\right)}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\cos{\\left(x \\right)}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x^{3} \\left(- x^{2} \\left(x \\cos{\\left(x \\right)} + 2 \\sin{\\left(x \\right)}\\right) \\sin{\\left(x \\right)} \\sin{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} + 2 x \\cos{\\left(x \\right)} \\cos{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} + 4 \\sin{\\left(x \\right)} \\cos{\\left(x^{2} \\sin{\\left(x \\right)} \\right)}\\right) \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} e^{x}, g(x) = x^{2} \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} e^{x}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "x^{3} \\left(x^{2} \\left(2 \\log{\\left(x \\right)} + 1\\right) \\log{\\left(x \\right)} + 4 \\log{\\left(x \\right)} + 2\\right) e^{x^{2} \\log{\\left(x \\right)}} \\log{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2}, g(x) = x. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Provide an integer within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2}", "g": "x", "x_value": "1", "correct_answer": "2", "answer_format": "integer"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x e^{x}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x e^{x}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(x^{2} \\left(\\frac{x \\sin{\\left(2 x \\right)}}{2} - \\cos{\\left(2 x \\right)} + 1\\right) + x \\cos{\\left(x \\right)} + 2 \\sin{\\left(x \\right)}\\right) e^{x^{2} \\sin{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{4}, g(x) = x^{\\frac{3}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{4}", "g": "x^{\\frac{3}{2}}", "x_value": null, "correct_answer": "6 x^{5}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\sin{\\left(\\sin{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "e^{x}", "x_value": null, "correct_answer": "- e^{x} \\sin{\\left(e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = x \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "x \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(- 2 x \\log{\\left(x \\cos{\\left(x \\right)} \\right)} \\sin{\\left(x \\right)} - x \\sin{\\left(x \\right)} + 2 \\log{\\left(x \\cos{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)} + \\cos{\\left(x \\right)}\\right) \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = x^{2} \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(- x^{2} \\left(x \\sin{\\left(x \\right)} - 2 \\cos{\\left(x \\right)}\\right) \\cos{\\left(x \\right)} \\cos{\\left(x^{2} \\cos{\\left(x \\right)} \\right)} - x \\sin{\\left(x \\right)} \\sin{\\left(x^{2} \\cos{\\left(x \\right)} \\right)} + 2 \\sin{\\left(x^{2} \\cos{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)}\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\sin{\\left(x \\right)}, g(x) = \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\sin{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "x_value": null, "correct_answer": "\\frac{\\left(\\log{\\left(x \\right)} \\cos{\\left(\\log{\\left(x \\right)} \\right)} + 2 \\sin{\\left(\\log{\\left(x \\right)} \\right)}\\right) \\log{\\left(x \\right)}}{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sqrt{x}, g(x) = x^{\\frac{5}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x^{\\frac{5}{2}}", "x_value": null, "correct_answer": "\\frac{5 \\sqrt{x^{\\frac{5}{2}}}}{4 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sin{\\left(x \\right)}, g(x) = x^{2}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{2}", "x_value": null, "correct_answer": "2 x \\cos{\\left(x^{2} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x, g(x) = x^{3}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x", "g": "x^{3}", "x_value": null, "correct_answer": "3 x^{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sqrt{x}, g(x) = x. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x", "x_value": null, "correct_answer": "\\frac{1}{2 \\sqrt{x}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = x e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "x e^{x}", "x_value": null, "correct_answer": "\\frac{3 \\left(x e^{x}\\right)^{\\frac{3}{2}} \\left(x + 1\\right)}{2 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "e^{x}", "x_value": null, "correct_answer": "- e^{x} \\sin{\\left(e^{x} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x^{\\frac{3}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x^{\\frac{3}{2}}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{x} \\left(\\log{\\left(x^{\\frac{3}{2}} \\right)} + 1\\right)}{2}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{\\frac{3}{2}}, g(x) = \\sin{\\left(x \\right)}. Find f△g at x = 1.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\nSubstitute x = 1.\n- Round to two decimal places within [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{\\frac{3}{2}}", "g": "\\sin{\\left(x \\right)}", "x_value": "1", "correct_answer": "0.74", "answer_format": "float"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x^{4}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x^{4}", "x_value": null, "correct_answer": "4 x^{3} \\left(\\log{\\left(x^{4} \\right)} + 1\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = x^{2} \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "x^{2} \\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(- x \\sin{\\left(x \\right)} + 2 \\cos{\\left(x \\right)}\\right) e^{x^{2} \\cos{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{6}, g(x) = x^{\\frac{5}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{6}", "g": "x^{\\frac{5}{2}}", "x_value": null, "correct_answer": "15 x^{14}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\left(\\sin{\\left(\\cos{\\left(x \\right)} \\right)} + \\cos{\\left(x \\right)} \\cos{\\left(\\cos{\\left(x \\right)} \\right)}\\right) \\sin{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = x^{4}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "x^{4}", "x_value": null, "correct_answer": "x^{7} \\left(8 \\log{\\left(x^{4} \\right)} + 4\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "\\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\cos{\\left(x \\right)}, g(x) = x^{4}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{4}", "x_value": null, "correct_answer": "- 4 x^{3} \\sin{\\left(x^{4} \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} e^{x}, g(x) = x. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} e^{x}", "g": "x", "x_value": null, "correct_answer": "x \\left(x + 2\\right) e^{x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x^{3} \\left(x \\sin{\\left(2 x \\right)} - 2 \\cos{\\left(2 x \\right)} + 2\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x e^{x}, g(x) = x^{2} \\log{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x e^{x}", "g": "x^{2} \\log{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(x^{2} \\left(2 \\log{\\left(x \\right)} + 1\\right) \\log{\\left(x \\right)} + 2 \\log{\\left(x \\right)} + 1\\right) e^{x^{2} \\log{\\left(x \\right)}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\log{\\left(x \\right)}, g(x) = x^{2} \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\log{\\left(x \\right)}", "g": "x^{2} \\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "x \\left(x \\log{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} \\cos{\\left(x \\right)} + x \\cos{\\left(x \\right)} + 2 \\log{\\left(x^{2} \\sin{\\left(x \\right)} \\right)} \\sin{\\left(x \\right)} + 2 \\sin{\\left(x \\right)}\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{2} \\log{\\left(x \\right)}, g(x) = x^{2}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{2} \\log{\\left(x \\right)}", "g": "x^{2}", "x_value": null, "correct_answer": "x^{3} \\left(4 \\log{\\left(x^{2} \\right)} + 2\\right)", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{4}, g(x) = e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{4}", "g": "e^{x}", "x_value": null, "correct_answer": "4 e^{4 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = x^{4}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "x^{4}", "x_value": null, "correct_answer": "4 x^{3} e^{x^{4}}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = \\sqrt{x}, g(x) = x^{\\frac{3}{2}}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x^{\\frac{3}{2}}", "x_value": null, "correct_answer": "\\frac{3 \\sqrt{x^{\\frac{3}{2}}}}{4 x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x^{3}, g(x) = \\sin{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x^{3}", "g": "\\sin{\\left(x \\right)}", "x_value": null, "correct_answer": "3 \\sin^{2}{\\left(x \\right)} \\cos{\\left(x \\right)}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = e^{x}, g(x) = x e^{x}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "e^{x}", "g": "x e^{x}", "x_value": null, "correct_answer": "\\left(x + 1\\right) e^{x e^{x} + x}", "answer_format": "latex"}}
{"data_source": "KorOperationUnicode25b3", "prompt": "Define that: f△g=(f(g(x)))′\n\nSolve the calculus puzzle:\n\n**Problem**: f(x) = x \\sin{\\left(x \\right)}, g(x) = \\cos{\\left(x \\right)}. Compute f△g.\n\n**Rules**:\n- Compute the derivative of f(g(x)).\n\n- Provide your answer in LaTeX enclosed in [[ ]].\n\n**Answer**: [[your answer here]]", "ground_truth": {"f": "x \\sin{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "x_value": null, "correct_answer": "- \\left(\\sin{\\left(\\cos{\\left(x \\right)} \\right)} + \\cos{\\left(x \\right)} \\cos{\\left(\\cos{\\left(x \\right)} \\right)}\\right) \\sin{\\left(x \\right)}", "answer_format": "latex"}}
Reference in a new issue View git blame Copy permalink