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InternBootcamp/examples/data/Intenbootcamp_eval/korOperationUnicode25a1.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

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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = x\n\nFind the numerical value of f□g at x = 1.5708.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x", "problem_type": "evaluate", "correct_answer": 0.0, "x_value": 1.5708}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 2.5577, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 7.7426, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 1.2929, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": -1.0, "x_value": 3.1416}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 4.7124.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 0.2122, "x_value": 4.7124}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 1.5708.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 12.2127, "x_value": 1.5708}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = x\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "x", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 0}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = x\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x", "problem_type": "evaluate", "correct_answer": 1.5642, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "2 x + e^{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = x^{3}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "x^{3}", "problem_type": "expression", "correct_answer": "6 x^{2}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 5.4255, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "3 x^{2} + e^{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": -0.4093, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 3.9658, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\sqrt{x}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\sqrt{x}", "problem_type": "evaluate", "correct_answer": 0.7071, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 0}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = x\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "x", "problem_type": "evaluate", "correct_answer": 7.2832, "x_value": 3.1416}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = \\tan{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\tan{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\tan^{2}{\\left(x \\right)} + 1 + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\frac{1}{x} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = \\tan{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "\\tan{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "- \\sin{\\left(x \\right)} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "2 x - \\sin{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\cos{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\cos{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "1 - \\sin{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = x\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "x", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\log{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\log{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 4.5, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 5.3583, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\tan^{2}{\\left(x \\right)} + 1 + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\log{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\log{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 12.5, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "2 x + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 3.1416, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\log{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.5708.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\log{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 8.0389, "x_value": 1.5708}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 1.0403, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "2 x + e^{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = x\n\nFind the numerical value of f□g at x = 4.7124.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "x", "problem_type": "evaluate", "correct_answer": 10.4248, "x_value": 4.7124}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 2.2779, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 0}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = \\log{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 1.0, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\tan{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\tan{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "e^{x} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 1.0, "x_value": 0}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "2 e^{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x", "problem_type": "evaluate", "correct_answer": 1.7071, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = x\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 3.7183, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 2.5708, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 3.5403, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 2.584, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\log{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\log{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 4.0, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "2 x + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "\\frac{1}{\\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "\\tan^{2}{\\left(x \\right)} + 1 + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 6.6015, "x_value": 3.1416}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 4.3536, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "2 x + e^{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x^{3}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{3}", "problem_type": "expression", "correct_answer": "3 x^{2} + \\cos{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = x\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "x", "problem_type": "evaluate", "correct_answer": 2.5708, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 29.609, "x_value": 3.1416}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 2.2779, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "3 x^{2} + e^{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + 1", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\tan{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\tan{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\tan^{2}{\\left(x \\right)} + 2", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "2 \\cos{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 0.0, "x_value": 0}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\frac{1}{x} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x", "problem_type": "expression", "correct_answer": "1 - \\sin{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 2.2779, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\sqrt{x}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\sqrt{x}", "problem_type": "evaluate", "correct_answer": 1.0403, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 1.0, "x_value": 0}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 23.1409, "x_value": 3.1416}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{x}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 1.8768, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 1.0, "x_value": 0}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\cos{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "e^{x} + \\cos{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = x^{3}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "x^{3}", "problem_type": "expression", "correct_answer": "3 x^{2} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 4.4255, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "2 x + \\cos{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 3.1416, "x_value": 0.7854}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "x", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\tan{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\tan{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\tan^{2}{\\left(x \\right)} + 1 + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = x^{3}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "x^{3}", "problem_type": "evaluate", "correct_answer": 17.7744, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 7.7426, "x_value": 2}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\cos{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\cos{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "e^{x} - \\sin{\\left(x \\right)}", "x_value": null}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 3.2586, "x_value": 1}}
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 7.2832, "x_value": 3.1416}}
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