mirror of
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64 lines
32 KiB
JSON
Executable file
64 lines
32 KiB
JSON
Executable file
{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{3 x}\ng(x) = 2 \\cos{\\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": "3 e^{3 x}", "g_latex": "2 \\cos{\\left(3 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{3 x} - 18 \\cos{\\left(3 x \\right)}", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 1\ng(x) = 3 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": "2 x^{2} + 2 x + 1", "g_latex": "3 x^{2} + 3 x + 3", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 2 x + 7", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{3 x}\ng(x) = x^{2} + x + 3\nCompute: f▽g = f(x) + g''(x)\nat x = -1.94\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{3 x}", "g_latex": "x^{2} + x + 3", "x_value": -1.94, "expected_num": 2.01, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + x + 1\ng(x) = 3 \\cos{\\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": "x^{2} + x + 1", "g_latex": "3 \\cos{\\left(3 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "x^{2} + x - 27 \\cos{\\left(3 x \\right)} + 1", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 2 x + 1\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": "x^{2} + 2 x + 1", "g_latex": "x^{2} + 3 x + 3", "x_value": null, "expected_num": null, "expected_str": "x^{2} + 2 x + 3", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\cos{\\left(3 x \\right)}\ng(x) = 2 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(3 x \\right)}", "g_latex": "2 x^{2} + 3 x + 1", "x_value": null, "expected_num": null, "expected_str": "\\cos{\\left(3 x \\right)} + 4", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{2 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^{2 x}", "g_latex": "\\sin{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "e^{2 x} - \\sin{\\left(x \\right)}", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\ng(x) = x^{2} + 2 x + 3\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": "2 e^{x}", "g_latex": "x^{2} + 2 x + 3", "x_value": -1.66, "expected_num": 2.38, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 3 x + 1\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": "x^{2} + 3 x + 1", "g_latex": "2 \\cos{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "x^{2} + 3 x - 2 \\cos{\\left(x \\right)} + 1", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 3 x + 2\ng(x) = 3 \\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": "x^{2} + 3 x + 2", "g_latex": "3 \\log{\\left(x e^{2} \\right)}", "x_value": null, "expected_num": null, "expected_str": "x^{2} + 3 x + 2 - \\frac{3}{x^{2}}", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\sin{\\left(x \\right)}\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 \\sin{\\left(x \\right)}", "g_latex": "\\log{\\left(e x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 \\sin{\\left(x \\right)} - \\frac{1}{x^{2}}", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\left(2 x \\right)}\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": "2 \\cos{\\left(2 x \\right)}", "g_latex": "2 x^{2} + 2 x + 1", "x_value": null, "expected_num": null, "expected_str": "2 \\cos{\\left(2 x \\right)} + 4", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 1\ng(x) = \\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 + 1", "g_latex": "\\log{\\left(10 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}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 2 x + 2\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": "x^{2} + 2 x + 2", "g_latex": "3 \\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "x^{2} + 2 x + 2 - \\frac{3}{x^{2}}", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\ng(x) = 3 \\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^{2 x}", "g_latex": "3 \\cos{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{2 x} - 3 \\cos{\\left(x \\right)}", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + x + 3\ng(x) = 2 \\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": "3 x^{2} + x + 3", "g_latex": "2 \\sin{\\left(3 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 x^{2} + x - 18 \\sin{\\left(3 x \\right)} + 3", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + x + 2\ng(x) = 2 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 x^{2} + x + 2", "g_latex": "2 x^{2} + x + 1", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + x + 6", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + x + 2\ng(x) = 2 x^{2} + 2 x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = -2.31\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 + 2", "g_latex": "2 x^{2} + 2 x + 1", "x_value": -2.31, "expected_num": 19.698, "expected_str": null, "precision": 3, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(2 x \\right)}\ng(x) = 3 \\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 \\sin{\\left(2 x \\right)}", "g_latex": "3 \\cos{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "\\left(4 \\sin{\\left(x \\right)} - 3\\right) \\cos{\\left(x \\right)}", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\ng(x) = 3 \\log{\\left(x e^{3} \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -2.59\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 e^{x}", "g_latex": "3 \\log{\\left(x e^{3} \\right)}", "x_value": -2.59, "expected_num": -0.297, "expected_str": null, "precision": 3, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\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 \\cos{\\left(2 x \\right)}", "g_latex": "2 \\log{\\left(10 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 \\cos{\\left(2 x \\right)} - \\frac{2}{x^{2}}", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 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": "e^{x}", "g_latex": "2 x^{2} + x + 3", "x_value": null, "expected_num": null, "expected_str": "e^{x} + 4", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 2 x + 1\ng(x) = 3 \\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": "x^{2} + 2 x + 1", "g_latex": "3 \\log{\\left(e x \\right)}", "x_value": null, "expected_num": null, "expected_str": "x^{2} + 2 x + 1 - \\frac{3}{x^{2}}", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{3 x}\ng(x) = 3 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": "2 e^{3 x}", "g_latex": "3 x^{2} + 2 x + 1", "x_value": null, "expected_num": null, "expected_str": "2 e^{3 x} + 6", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{2 x}\ng(x) = 3 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": "2 e^{2 x}", "g_latex": "3 x^{2} + 2 x + 3", "x_value": null, "expected_num": null, "expected_str": "2 e^{2 x} + 6", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\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": "3 e^{2 x}", "g_latex": "\\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{2 x} - \\frac{1}{x^{2}}", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\sin{\\left(x \\right)}\ng(x) = x^{2} + 2 x + 1\nCompute: f▽g = f(x) + g''(x)\nat x = -0.1\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\sin{\\left(x \\right)}", "g_latex": "x^{2} + 2 x + 1", "x_value": -0.1, "expected_num": 1.7, "expected_str": null, "precision": 3, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\sin{\\left(3 x \\right)}\ng(x) = 2 \\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 \\sin{\\left(3 x \\right)}", "g_latex": "2 \\log{\\left(x e^{3} \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 \\sin{\\left(3 x \\right)} - \\frac{2}{x^{2}}", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + 3 x + 3\ng(x) = 2 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.97\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 \\cos{\\left(x \\right)}", "x_value": 0.97, "expected_num": 7.6, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{3 x}\ng(x) = 3 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": "2 e^{3 x}", "g_latex": "3 x^{2} + x + 3", "x_value": null, "expected_num": null, "expected_str": "2 e^{3 x} + 6", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 3 x + 1\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": "x^{2} + 3 x + 1", "g_latex": "2 \\log{\\left(e x \\right)}", "x_value": null, "expected_num": null, "expected_str": "x^{2} + 3 x + 1 - \\frac{2}{x^{2}}", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{3 x}\ng(x) = \\log{\\left(100 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 2.09\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": "\\log{\\left(100 x \\right)}", "x_value": 2.09, "expected_num": 528.25, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{3 x}\ng(x) = 3 x^{2} + x + 3\nCompute: f▽g = f(x) + g''(x)\nat x = -0.79\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 x^{2} + x + 3", "x_value": -0.79, "expected_num": 6.09, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{3 x}\ng(x) = \\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 e^{3 x}", "g_latex": "\\sin{\\left(2 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 e^{3 x} - 4 \\sin{\\left(2 x \\right)}", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\ng(x) = 3 \\log{\\left(x e^{3} \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -1.13\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 \\log{\\left(x e^{3} \\right)}", "x_value": -1.13, "expected_num": -1.7, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{3 x}\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": "3 e^{3 x}", "g_latex": "3 \\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 e^{3 x} - \\frac{3}{x^{2}}", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = \\sin{\\left(2 x \\right)}\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": "\\sin{\\left(2 x \\right)}", "g_latex": "2 x^{2} + 3 x + 2", "x_value": null, "expected_num": null, "expected_str": "\\sin{\\left(2 x \\right)} + 4", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\left(2 x \\right)}\ng(x) = 3 x^{2} + 2 x + 3\nCompute: f▽g = f(x) + g''(x)\nat x = 1.43\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 \\cos{\\left(2 x \\right)}", "g_latex": "3 x^{2} + 2 x + 3", "x_value": 1.43, "expected_num": 4.08, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 3 x + 3\ng(x) = 3 \\log{\\left(10 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": "x^{2} + 3 x + 3", "g_latex": "3 \\log{\\left(10 x \\right)}", "x_value": -0.17, "expected_num": -101.29, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"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}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\ng(x) = 2 \\log{\\left(10 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.52\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": "2 \\log{\\left(10 x \\right)}", "x_value": 0.52, "expected_num": 1.09, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{2 x}\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": "e^{2 x}", "g_latex": "\\log{\\left(x e^{2} \\right)}", "x_value": null, "expected_num": null, "expected_str": "e^{2 x} - \\frac{1}{x^{2}}", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\ng(x) = 2 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": "3 e^{2 x}", "g_latex": "2 x^{2} + 3 x + 1", "x_value": null, "expected_num": null, "expected_str": "3 e^{2 x} + 4", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + 3 x + 1\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": "3 x^{2} + 3 x + 1", "g_latex": "\\sin{\\left(x \\right)}", "x_value": null, "expected_num": null, "expected_str": "3 x^{2} + 3 x - \\sin{\\left(x \\right)} + 1", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\left(3 x \\right)}\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": "2 \\cos{\\left(3 x \\right)}", "g_latex": "2 x^{2} + 2 x + 1", "x_value": null, "expected_num": null, "expected_str": "2 \\cos{\\left(3 x \\right)} + 4", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 2\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": "2 x^{2} + 2 x + 2", "g_latex": "\\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 2 x + 2 - \\frac{1}{x^{2}}", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{x}\ng(x) = x^{2} + 2 x + 2\nCompute: f▽g = f(x) + g''(x)\nat x = -0.6\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": "x^{2} + 2 x + 2", "x_value": -0.6, "expected_num": 3.65, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 2\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": "2 x^{2} + 2 x + 2", "g_latex": "x^{2} + x + 3", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 2 x + 4", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\cos{\\left(3 x \\right)}\ng(x) = 3 \\sin{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = 0.95\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 \\cos{\\left(3 x \\right)}", "g_latex": "3 \\sin{\\left(2 x \\right)}", "x_value": 0.95, "expected_num": -14.229, "expected_str": null, "precision": 3, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + 2 x + 2\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 x^{2} + 2 x + 2", "g_latex": "3 \\sin{\\left(3 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 2 x - 27 \\sin{\\left(3 x \\right)} + 2", "precision": 5, "is_numeric": false}}
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{"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 + 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": "2 x^{2} + 2 x + 1", "g_latex": "2 x^{2} + 2 x + 3", "x_value": null, "expected_num": null, "expected_str": "2 x^{2} + 2 x + 5", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 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": "3 e^{x}", "g_latex": "x^{2} + 3 x + 3", "x_value": null, "expected_num": null, "expected_str": "3 e^{x} + 2", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = e^{2 x}\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": "e^{2 x}", "g_latex": "2 \\log{\\left(e x \\right)}", "x_value": null, "expected_num": null, "expected_str": "e^{2 x} - \\frac{2}{x^{2}}", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{x}\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": "2 e^{x}", "g_latex": "\\log{\\left(100 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "2 e^{x} - \\frac{1}{x^{2}}", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 e^{3 x}\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": "2 e^{3 x}", "g_latex": "3 x^{2} + 3 x + 2", "x_value": null, "expected_num": null, "expected_str": "2 e^{3 x} + 6", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{2 x}\ng(x) = 2 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": "3 e^{2 x}", "g_latex": "2 x^{2} + 3 x + 3", "x_value": null, "expected_num": null, "expected_str": "3 e^{2 x} + 4", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 \\cos{\\left(3 x \\right)}\ng(x) = 3 \\cos{\\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 \\cos{\\left(3 x \\right)}", "g_latex": "3 \\cos{\\left(3 x \\right)}", "x_value": null, "expected_num": null, "expected_str": "- 25 \\cos{\\left(3 x \\right)}", "precision": 3, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 2 x^{2} + x + 1\ng(x) = x^{2} + 2 x + 3\nCompute: f▽g = f(x) + g''(x)\nat x = 2.46\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "2 x^{2} + x + 1", "g_latex": "x^{2} + 2 x + 3", "x_value": 2.46, "expected_num": 17.563, "expected_str": null, "precision": 3, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 \\cos{\\left(3 x \\right)}\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": "3 \\cos{\\left(3 x \\right)}", "g_latex": "2 x^{2} + 3 x + 2", "x_value": null, "expected_num": null, "expected_str": "3 \\cos{\\left(3 x \\right)} + 4", "precision": 5, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + 2 x + 2\ng(x) = 2 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": "3 x^{2} + 2 x + 2", "g_latex": "2 x^{2} + x + 2", "x_value": null, "expected_num": null, "expected_str": "3 x^{2} + 2 x + 6", "precision": 2, "is_numeric": false}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 e^{x}\ng(x) = x^{2} + x + 2\nCompute: f▽g = f(x) + g''(x)\nat x = 1.83\nProvide a numerical value rounded to 3 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "3 e^{x}", "g_latex": "x^{2} + x + 2", "x_value": 1.83, "expected_num": 20.702, "expected_str": null, "precision": 3, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + x + 3\ng(x) = \\sin{\\left(2 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -2.41\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 + 3", "g_latex": "\\sin{\\left(2 x \\right)}", "x_value": -2.41, "expected_num": 14.04, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = 3 x^{2} + 3 x + 2\ng(x) = 2 \\cos{\\left(3 x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -0.49\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(3 x \\right)}", "x_value": -0.49, "expected_num": -0.56, "expected_str": null, "precision": 2, "is_numeric": true}}
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{"data_source": "KorOperationUnicode25bd", "prompt": "Solve the differential operator problem:\nGiven:\nf(x) = x^{2} + 3 x + 3\ng(x) = 3 \\cos{\\left(x \\right)}\nCompute: f▽g = f(x) + g''(x)\nat x = -2.84\nProvide a numerical value rounded to 2 decimal places.\nFormat your answer within double square brackets: [[answer]]", "ground_truth": {"f_latex": "x^{2} + 3 x + 3", "g_latex": "3 \\cos{\\left(x \\right)}", "x_value": -2.84, "expected_num": 5.41, "expected_str": null, "precision": 2, "is_numeric": true}}
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