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InternBootcamp/examples/data/Intenbootcamp_eval/korOperationUnicode25bd.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": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\sin{\\left(2 x \\right)}\ng(x) = 3 \\cos{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -2.96\nProvide a numerical value rounded to 5 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\sin{\\left(2 x \\right)}", "g_latex": "3 \\cos{\\left(3 x \\right)}", "x_value": -2.96, "expected_num": 24.1573, "expected_str": null, "precision": 5, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + x + 3\ng(x) = \\log{\\left(e x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.57\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "x^{2} + x + 3", "g_latex": "\\log{\\left(e x \\right)}", "x_value": -1.57, "expected_num": 3.489, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\sin{\\left(2 x \\right)}\ng(x) = 2 \\log{\\left(e x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\sin{\\left(2 x \\right)}", "g_latex": "2 \\log{\\left(e x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 \\sin{\\left(2 x \\right)} - \\frac{2}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{3 x}\ng(x) = 3 \\sin{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.11\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{3 x}", "g_latex": "3 \\sin{\\left(3 x \\right)}", "x_value": -1.11, "expected_num": -4.99, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = 3 x^{2} + 3 x + 2\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\sin{\\left(x \\right)}", "g_latex": "3 x^{2} + 3 x + 2", "x_value": null, "expected_num": null, "expected_str": "\\sin{\\left(x \\right)} + 6", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{2 x}\ng(x) = 3 \\log{\\left(x e^{3} \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{2 x}", "g_latex": "3 \\log{\\left(x e^{3} \\right)}", "x_value": null, "expected_num": null, "expected_str": "e^{2 x} - \\frac{3}{x^{2}}", "precision": 3, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\left(x \\right)}\ng(x) = 3 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -0.15\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\cos{\\left(x \\right)}", "g_latex": "3 \\cos{\\left(x \\right)}", "x_value": -0.15, "expected_num": -0.989, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 3 x + 1\ng(x) = \\log{\\left(e x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 3 x + 1", "g_latex": "\\log{\\left(e x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 3 x + 1 - \\frac{1}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\ng(x) = \\cos{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{2 x}", "g_latex": "\\cos{\\left(2 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{2 x} - 4 \\cos{\\left(2 x \\right)}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = 2 \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\cos{\\left(x \\right)}", "g_latex": "2 \\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "\\cos{\\left(x \\right)} - \\frac{2}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\ng(x) = 3 \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.54\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{2 x}", "g_latex": "3 \\log{\\left(1000 x \\right)}", "x_value": -1.54, "expected_num": -1.13, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 3 x + 1\ng(x) = 3 \\log{\\left(10 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.23\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 3 x + 1", "g_latex": "3 \\log{\\left(10 x \\right)}", "x_value": -1.23, "expected_num": -1.65, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 3 x + 3\ng(x) = 3 \\sin{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 2.72\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 3 x + 3", "g_latex": "3 \\sin{\\left(x \\right)}", "x_value": 2.72, "expected_num": 24.729, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\left(3 x \\right)}\ng(x) = 2 \\cos{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.2\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\cos{\\left(3 x \\right)}", "g_latex": "2 \\cos{\\left(2 x \\right)}", "x_value": 0.2, "expected_num": -5.718, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{x}\ng(x) = \\sin{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{x}", "g_latex": "\\sin{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "e^{x} - \\sin{\\left(x \\right)}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{2 x}\ng(x) = 3 \\cos{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{2 x}", "g_latex": "3 \\cos{\\left(2 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 e^{2 x} - 12 \\cos{\\left(2 x \\right)}", "precision": 3, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(2 x \\right)}\ng(x) = 2 \\log{\\left(10 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\sin{\\left(2 x \\right)}", "g_latex": "2 \\log{\\left(10 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 \\sin{\\left(2 x \\right)} - \\frac{2}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + x + 1\ng(x) = \\cos{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 x^{2} + x + 1", "g_latex": "\\cos{\\left(2 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 x^{2} + x - 4 \\cos{\\left(2 x \\right)} + 1", "precision": 3, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\sin{\\left(2 x \\right)}\ng(x) = 2 \\sin{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\sin{\\left(2 x \\right)}", "g_latex": "2 \\sin{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 \\left(3 \\cos{\\left(x \\right)} - 1\\right) \\sin{\\left(x \\right)}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\cos{\\left(2 x \\right)}\ng(x) = x^{2} + 3 x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = 0.29\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\cos{\\left(2 x \\right)}", "g_latex": "x^{2} + 3 x + 1", "x_value": 0.29, "expected_num": 2.836, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{x}\ng(x) = x^{2} + 2 x + 2\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{x}", "g_latex": "x^{2} + 2 x + 2", "x_value": null, "expected_num": null, "expected_str": "e^{x} + 2", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{x}\ng(x) = 2 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.14\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{x}", "g_latex": "2 \\cos{\\left(x \\right)}", "x_value": -1.14, "expected_num": 0.12, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(3 x \\right)}\ng(x) = 3 x^{2} + x + 3\nCompute: f▽g = f(x) + g''(x)\nat x = -2.85\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\sin{\\left(3 x \\right)}", "g_latex": "3 x^{2} + x + 3", "x_value": -2.85, "expected_num": 4.465, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + x + 1\ng(x) = \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "x^{2} + x + 1", "g_latex": "\\log{\\left(1000 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "x^{2} + x + 1 - \\frac{1}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{x}\ng(x) = x^{2} + 3 x + 3\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{x}", "g_latex": "x^{2} + 3 x + 3", "x_value": null, "expected_num": null, "expected_str": "e^{x} + 2", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\cos{\\left(2 x \\right)}\ng(x) = \\log{\\left(x e^{3} \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.6\nProvide a numerical value rounded to 5 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\cos{\\left(2 x \\right)}", "g_latex": "\\log{\\left(x e^{3} \\right)}", "x_value": -1.6, "expected_num": -3.38551, "expected_str": null, "precision": 5, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{2 x}\ng(x) = 2 \\sin{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 2.75\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{2 x}", "g_latex": "2 \\sin{\\left(2 x \\right)}", "x_value": 2.75, "expected_num": 250.336, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{3 x}\ng(x) = 3 \\sin{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 2.31\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{3 x}", "g_latex": "3 \\sin{\\left(3 x \\right)}", "x_value": 2.31, "expected_num": 1006.22, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\ng(x) = \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{2 x}", "g_latex": "\\log{\\left(1000 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{2 x} - \\frac{1}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 3\ng(x) = 3 \\log{\\left(10 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 2 x + 3", "g_latex": "3 \\log{\\left(10 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 2 x + 3 - \\frac{3}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{3 x}\ng(x) = 2 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{3 x}", "g_latex": "2 \\cos{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{3 x} - 2 \\cos{\\left(x \\right)}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\sin{\\left(3 x \\right)}\ng(x) = 2 x^{2} + 3 x + 2\nCompute: f▽g = f(x) + g''(x)\nat x = -1.92\nProvide a numerical value rounded to 5 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\sin{\\left(3 x \\right)}", "g_latex": "2 x^{2} + 3 x + 2", "x_value": -1.92, "expected_num": 5.49893, "expected_str": null, "precision": 5, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\ng(x) = 3 x^{2} + x + 1\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{x}", "g_latex": "3 x^{2} + x + 1", "x_value": null, "expected_num": null, "expected_str": "2 e^{x} + 6", "precision": 3, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + x + 1\ng(x) = 3 x^{2} + x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = 1.99\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "x^{2} + x + 1", "g_latex": "3 x^{2} + x + 1", "x_value": 1.99, "expected_num": 12.95, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + x + 1\ng(x) = \\log{\\left(x e^{2} \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + x + 1", "g_latex": "\\log{\\left(x e^{2} \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + x + 1 - \\frac{1}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 1\ng(x) = 2 x^{2} + 2 x + 2\nCompute: f▽g = f(x) + g''(x)\nat x = -1.45\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 2 x + 1", "g_latex": "2 x^{2} + 2 x + 2", "x_value": -1.45, "expected_num": 6.3, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\sin{\\left(3 x \\right)}\ng(x) = 2 \\sin{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -2.51\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\sin{\\left(3 x \\right)}", "g_latex": "2 \\sin{\\left(3 x \\right)}", "x_value": -2.51, "expected_num": 14.22, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{3 x}\ng(x) = \\log{\\left(x e^{3} \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -0.29\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{3 x}", "g_latex": "\\log{\\left(x e^{3} \\right)}", "x_value": -0.29, "expected_num": -11.472, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{x}\ng(x) = 2 x^{2} + 2 x + 1\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{x}", "g_latex": "2 x^{2} + 2 x + 1", "x_value": null, "expected_num": null, "expected_str": "3 e^{x} + 4", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\ng(x) = 2 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{x}", "g_latex": "2 \\cos{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 e^{x} - 2 \\cos{\\left(x \\right)}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{3 x}\ng(x) = 2 \\sin{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{3 x}", "g_latex": "2 \\sin{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 e^{3 x} - 2 \\sin{\\left(x \\right)}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{2 x}\ng(x) = 3 x^{2} + x + 2\nCompute: f▽g = f(x) + g''(x)\nat x = 1.65\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{2 x}", "g_latex": "3 x^{2} + x + 2", "x_value": 1.65, "expected_num": 60.225, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + x + 2\ng(x) = 2 \\log{\\left(e x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 x^{2} + x + 2", "g_latex": "2 \\log{\\left(e x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 x^{2} + x + 2 - \\frac{2}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + x + 1\ng(x) = \\log{\\left(x e^{3} \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -2.31\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "x^{2} + x + 1", "g_latex": "\\log{\\left(x e^{3} \\right)}", "x_value": -2.31, "expected_num": 3.84, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(2 x \\right)}\ng(x) = 3 \\sin{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\sin{\\left(2 x \\right)}", "g_latex": "3 \\sin{\\left(3 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 \\sin{\\left(2 x \\right)} - 27 \\sin{\\left(3 x \\right)}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\sin{\\left(2 x \\right)}\ng(x) = 2 x^{2} + 2 x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = 1.53\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\sin{\\left(2 x \\right)}", "g_latex": "2 x^{2} + 2 x + 1", "x_value": 1.53, "expected_num": 4.24, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{2 x}\ng(x) = 3 \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.15\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{2 x}", "g_latex": "3 \\log{\\left(100 x \\right)}", "x_value": 0.15, "expected_num": -130.63, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\ng(x) = 3 \\cos{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -0.45\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{x}", "g_latex": "3 \\cos{\\left(3 x \\right)}", "x_value": -0.45, "expected_num": -4.64, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + 3 x + 2\ng(x) = 2 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.13\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 x^{2} + 3 x + 2", "g_latex": "2 \\cos{\\left(x \\right)}", "x_value": 0.13, "expected_num": 0.46, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = 3 \\log{\\left(e x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.83\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\cos{\\left(x \\right)}", "g_latex": "3 \\log{\\left(e x \\right)}", "x_value": -1.83, "expected_num": -1.15, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = \\cos{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -0.17\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\cos{\\left(x \\right)}", "g_latex": "\\cos{\\left(3 x \\right)}", "x_value": -0.17, "expected_num": -6.87, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\cos{\\left(3 x \\right)}\ng(x) = \\log{\\left(x e^{2} \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\cos{\\left(3 x \\right)}", "g_latex": "\\log{\\left(x e^{2} \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 \\cos{\\left(3 x \\right)} - \\frac{1}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + x + 3\ng(x) = 3 \\cos{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.58\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + x + 3", "g_latex": "3 \\cos{\\left(3 x \\right)}", "x_value": -1.58, "expected_num": 5.67, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\cos{\\left(x \\right)}\ng(x) = x^{2} + x + 3\nCompute: f▽g = f(x) + g''(x)\nat x = 2.6\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\cos{\\left(x \\right)}", "g_latex": "x^{2} + x + 3", "x_value": 2.6, "expected_num": -0.571, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{3 x}\ng(x) = \\log{\\left(x e^{3} \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{3 x}", "g_latex": "\\log{\\left(x e^{3} \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 e^{3 x} - \\frac{1}{x^{2}}", "precision": 3, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{3 x}\ng(x) = \\log{\\left(x e^{3} \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{3 x}", "g_latex": "\\log{\\left(x e^{3} \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 e^{3 x} - \\frac{1}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(2 x \\right)}\ng(x) = x^{2} + 3 x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = 1.31\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\sin{\\left(2 x \\right)}", "g_latex": "x^{2} + 3 x + 1", "x_value": 1.31, "expected_num": 3.0, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{2 x}\ng(x) = 2 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{2 x}", "g_latex": "2 \\cos{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "e^{2 x} - 2 \\cos{\\left(x \\right)}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\cos{\\left(2 x \\right)}\ng(x) = 2 x^{2} + 2 x + 3\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\cos{\\left(2 x \\right)}", "g_latex": "2 x^{2} + 2 x + 3", "x_value": null, "expected_num": null, "expected_str": "3 \\cos{\\left(2 x \\right)} + 4", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{x}\ng(x) = 2 x^{2} + x + 3\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{x}", "g_latex": "2 x^{2} + x + 3", "x_value": null, "expected_num": null, "expected_str": "3 e^{x} + 4", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{x}\ng(x) = 3 x^{2} + 2 x + 2\nCompute: f▽g = f(x) + g''(x)\nat x = -1.66\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{x}", "g_latex": "3 x^{2} + 2 x + 2", "x_value": -1.66, "expected_num": 6.57, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{2 x}\ng(x) = x^{2} + x + 3\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{2 x}", "g_latex": "x^{2} + x + 3", "x_value": null, "expected_num": null, "expected_str": "e^{2 x} + 2", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(x \\right)}\ng(x) = 2 \\log{\\left(10 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 1.21\nProvide a numerical value rounded to 5 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\sin{\\left(x \\right)}", "g_latex": "2 \\log{\\left(10 x \\right)}", "x_value": 1.21, "expected_num": 0.50521, "expected_str": null, "precision": 5, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\cos{\\left(3 x \\right)}\ng(x) = 2 x^{2} + 3 x + 3\nCompute: f▽g = f(x) + g''(x)\nat x = 2.55\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\cos{\\left(3 x \\right)}", "g_latex": "2 x^{2} + 3 x + 3", "x_value": 2.55, "expected_num": 4.203, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + 3 x + 2\ng(x) = 3 \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 2.71\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 x^{2} + 3 x + 2", "g_latex": "3 \\log{\\left(1000 x \\right)}", "x_value": 2.71, "expected_num": 31.75, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(2 x \\right)}\ng(x) = 3 \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\sin{\\left(2 x \\right)}", "g_latex": "3 \\log{\\left(1000 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 \\sin{\\left(2 x \\right)} - \\frac{3}{x^{2}}", "precision": 3, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{x}\ng(x) = 3 x^{2} + x + 2\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{x}", "g_latex": "3 x^{2} + x + 2", "x_value": null, "expected_num": null, "expected_str": "e^{x} + 6", "precision": 3, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\ng(x) = 2 x^{2} + 3 x + 2\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{x}", "g_latex": "2 x^{2} + 3 x + 2", "x_value": null, "expected_num": null, "expected_str": "2 e^{x} + 4", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x^{2} + 3 x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = 1.08\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\sin{\\left(x \\right)}", "g_latex": "x^{2} + 3 x + 1", "x_value": 1.08, "expected_num": 2.88, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\sin{\\left(3 x \\right)}\ng(x) = \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -0.92\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\sin{\\left(3 x \\right)}", "g_latex": "\\log{\\left(1000 x \\right)}", "x_value": -0.92, "expected_num": -1.55, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 2 x + 1\ng(x) = \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "x^{2} + 2 x + 1", "g_latex": "\\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "x^{2} + 2 x + 1 - \\frac{1}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{2 x}\ng(x) = x^{2} + 2 x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = 1.93\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{2 x}", "g_latex": "x^{2} + 2 x + 1", "x_value": 1.93, "expected_num": 96.93, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 3 x + 2\ng(x) = 2 \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.6\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 3 x + 2", "g_latex": "2 \\log{\\left(100 x \\right)}", "x_value": -1.6, "expected_num": 1.54, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\cos{\\left(2 x \\right)}\ng(x) = x^{2} + 3 x + 1\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\cos{\\left(2 x \\right)}", "g_latex": "x^{2} + 3 x + 1", "x_value": null, "expected_num": null, "expected_str": "\\cos{\\left(2 x \\right)} + 2", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{x}\ng(x) = 2 x^{2} + x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = 2.82\nProvide a numerical value rounded to 5 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{x}", "g_latex": "2 x^{2} + x + 1", "x_value": 2.82, "expected_num": 54.33055, "expected_str": null, "precision": 5, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(2 x \\right)}\ng(x) = \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.79\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\sin{\\left(2 x \\right)}", "g_latex": "\\log{\\left(1000 x \\right)}", "x_value": -1.79, "expected_num": 0.537, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{x}\ng(x) = 2 \\log{\\left(10 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{x}", "g_latex": "2 \\log{\\left(10 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "e^{x} - \\frac{2}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 1\ng(x) = \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 2 x + 1", "g_latex": "\\log{\\left(1000 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 2 x + 1 - \\frac{1}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 3\ng(x) = 3 x^{2} + x + 2\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 2 x + 3", "g_latex": "3 x^{2} + x + 2", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 2 x + 9", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 3 x + 2\ng(x) = 3 x^{2} + 3 x + 2\nCompute: f▽g = f(x) + g''(x)\nat x = -2.75\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 3 x + 2", "g_latex": "3 x^{2} + 3 x + 2", "x_value": -2.75, "expected_num": 14.88, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 3 x + 1\ng(x) = 3 x^{2} + 2 x + 2\nCompute: f▽g = f(x) + g''(x)\nat x = 1.43\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 3 x + 1", "g_latex": "3 x^{2} + 2 x + 2", "x_value": 1.43, "expected_num": 15.38, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 2 x + 3\ng(x) = \\cos{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -0.01\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "x^{2} + 2 x + 3", "g_latex": "\\cos{\\left(2 x \\right)}", "x_value": -0.01, "expected_num": -1.02, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{3 x}\ng(x) = 2 \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 2.25\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{3 x}", "g_latex": "2 \\log{\\left(100 x \\right)}", "x_value": 2.25, "expected_num": 853.66, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{x}\ng(x) = 2 \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "e^{x}", "g_latex": "2 \\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "e^{x} - \\frac{2}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 2\ng(x) = 3 \\log{\\left(10 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.21\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 2 x + 2", "g_latex": "3 \\log{\\left(10 x \\right)}", "x_value": 0.21, "expected_num": -65.519, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\left(3 x \\right)}\ng(x) = x^{2} + x + 2\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\cos{\\left(3 x \\right)}", "g_latex": "x^{2} + x + 2", "x_value": null, "expected_num": null, "expected_str": "2 \\cos{\\left(3 x \\right)} + 2", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\left(3 x \\right)}\ng(x) = 3 \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\cos{\\left(3 x \\right)}", "g_latex": "3 \\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 \\cos{\\left(3 x \\right)} - \\frac{3}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\cos{\\left(x \\right)}\ng(x) = 2 \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.56\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\cos{\\left(x \\right)}", "g_latex": "2 \\log{\\left(1000 x \\right)}", "x_value": 0.56, "expected_num": -3.836, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{x}\ng(x) = 2 \\log{\\left(1000 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{x}", "g_latex": "2 \\log{\\left(1000 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{x} - \\frac{2}{x^{2}}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{3 x}\ng(x) = \\log{\\left(e x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{3 x}", "g_latex": "\\log{\\left(e x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{3 x} - \\frac{1}{x^{2}}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 3 x + 1\ng(x) = 2 x^{2} + 2 x + 2\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + 3 x + 1", "g_latex": "2 x^{2} + 2 x + 2", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 3 x + 5", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\cos{\\left(3 x \\right)}\ng(x) = 2 \\log{\\left(10 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.16\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "\\cos{\\left(3 x \\right)}", "g_latex": "2 \\log{\\left(10 x \\right)}", "x_value": 0.16, "expected_num": -77.24, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + x + 2\ng(x) = \\log{\\left(e x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 1.65\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 x^{2} + x + 2", "g_latex": "\\log{\\left(e x \\right)}", "x_value": 1.65, "expected_num": 11.45, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\ng(x) = \\sin{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{x}", "g_latex": "\\sin{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 e^{x} - \\sin{\\left(x \\right)}", "precision": 2, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\ng(x) = 2 x^{2} + 2 x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = 2.85\nProvide a numerical value rounded to 5 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{2 x}", "g_latex": "2 x^{2} + 2 x + 1", "x_value": 2.85, "expected_num": 900.6022, "expected_str": null, "precision": 5, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{3 x}\ng(x) = 2 \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{3 x}", "g_latex": "2 \\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{3 x} - \\frac{2}{x^{2}}", "precision": 3, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\cos{\\left(3 x \\right)}\ng(x) = \\cos{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\cos{\\left(3 x \\right)}", "g_latex": "\\cos{\\left(2 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "- 4 \\cos{\\left(2 x \\right)} + 3 \\cos{\\left(3 x \\right)}", "precision": 5, "is_numeric": false}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + 3 x + 3\ng(x) = 2 \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 1.39\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 x^{2} + 3 x + 3", "g_latex": "2 \\log{\\left(100 x \\right)}", "x_value": 1.39, "expected_num": 11.93, "expected_str": null, "precision": 2, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + x + 3\ng(x) = 3 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 2.38\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 x^{2} + x + 3", "g_latex": "3 \\cos{\\left(x \\right)}", "x_value": 2.38, "expected_num": 24.544, "expected_str": null, "precision": 3, "is_numeric": true}}
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(x \\right)}\ng(x) = 3 \\sin{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nProvide the result as a LaTeX mathematical expression.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\sin{\\left(x \\right)}", "g_latex": "3 \\sin{\\left(2 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 \\sin{\\left(x \\right)} - 12 \\sin{\\left(2 x \\right)}", "precision": 2, "is_numeric": false}}
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