{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 4◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 4, "b": 5, "operator": "◆", "correct_answer": 5.797878220644789}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 1●3.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 1, "b": 3, "operator": "●", "correct_answer": 5.299649023251971}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute 0●3.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": 0, "b": 3, "operator": "●", "correct_answer": -3.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 1◆2.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 1, "b": 2, "operator": "◆", "correct_answer": 6.693147180559945}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^4, compute -1◆1.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^4", "a": -1, "b": 1, "operator": "◆", "correct_answer": 6.4}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -4◆2.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -4, "b": 2, "operator": "◆", "correct_answer": 6.1524949315177535}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, a◆3 = 16. Find a.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "x^3", "known_var": "b", "known_value": 3, "target_var": "a", "operator": "◆", "result": 16, "correct_answers": [2.53044, -2.53044]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -5★-1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -5, "b": -1, "operator": "★", "correct_answer": 4.3905620875658995}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -1x, compute -3★-1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-1x", "a": -3, "b": -1, "operator": "★", "correct_answer": 10.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -2●4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -2, "b": 4, "operator": "●", "correct_answer": 6.23749678431647}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -4●-1.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -4, "b": -1, "operator": "●", "correct_answer": 4.613705638880109}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute -5◆-4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": -5, "b": -4, "operator": "◆", "correct_answer": -86.25}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, a◆4 = 5. Find a.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "b", "known_value": 4, "target_var": "a", "operator": "◆", "result": 5, "correct_answers": [10.873127]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -5◆-1.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -5, "b": -1, "operator": "◆", "correct_answer": 4.3905620875658995}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -5◆-4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -5, "b": -4, "operator": "◆", "correct_answer": 5.77685644868579}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 0●1.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 0, "b": 1, "operator": "●", "correct_answer": 6.459697694131861}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 2x, a◆-5 = 13. Find a.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "2x", "known_var": "b", "known_value": -5, "target_var": "a", "operator": "◆", "result": 13, "correct_answers": [-4.242641, 4.242641]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, b●-4 = 13. Find b.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "-2x", "known_var": "a", "known_value": -4, "target_var": "b", "operator": "●", "result": 13, "correct_answers": [3.0, -3.0]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, a★3 = 5. Find a.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "x^2", "known_var": "b", "known_value": 3, "target_var": "a", "operator": "★", "result": 5, "correct_answers": [3.107233]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -3●0.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -3, "b": 0, "operator": "●", "correct_answer": 4.010007503399555}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -4◆-3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -4, "b": -3, "operator": "◆", "correct_answer": 5.712317927548219}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 4●5.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 4, "b": 5, "operator": "●", "correct_answer": 6.22314355131421}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, b●-3 = 11. Find b.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "x^3", "known_var": "a", "known_value": -3, "target_var": "b", "operator": "●", "result": 11, "correct_answers": [3.170154, -3.170154]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, a●5 = 20. Find a.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "b", "known_value": 5, "target_var": "a", "operator": "●", "result": 20, "correct_answers": [4e-06]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -1x, compute -3★4.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-1x", "a": -3, "b": 4, "operator": "★", "correct_answer": 2.5}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1x, compute -5●-4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1x", "a": -5, "b": -4, "operator": "●", "correct_answer": 1.5}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, a★5 = 19. Find a.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "x^2", "known_var": "b", "known_value": 5, "target_var": "a", "operator": "★", "result": 19, "correct_answers": [4.414005]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -3◆0.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -3, "b": 0, "operator": "◆", "correct_answer": 4.010007503399555}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute -5◆2.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": -5, "b": 2, "operator": "◆", "correct_answer": 27.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -1x, b★-4 = 13. Find b.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "-1x", "known_var": "a", "known_value": -4, "target_var": "b", "operator": "★", "result": 13, "correct_answers": [1.414214, -1.414214]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -1●1.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -1, "b": 1, "operator": "●", "correct_answer": 6.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -3★-1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -3, "b": -1, "operator": "★", "correct_answer": 4.90138771133189}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 0★3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 0, "b": 3, "operator": "★", "correct_answer": 6.141120008059867}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 2x, compute 2◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "2x", "a": 2, "b": 5, "operator": "◆", "correct_answer": 27.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, a◆0 = 12. Find a.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "x^2", "known_var": "b", "known_value": 0, "target_var": "a", "operator": "◆", "result": 12, "correct_answers": [-2.620741]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -2●4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -2, "b": 4, "operator": "●", "correct_answer": 6.1524949315177535}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 3★4.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 3, "b": 4, "operator": "★", "correct_answer": 5.102077496632204}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -1●0.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -1, "b": 0, "operator": "●", "correct_answer": 5.540302305868139}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 3x, compute 2★3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "3x", "a": 2, "b": 3, "operator": "★", "correct_answer": 13.5}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -5●-2.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -5, "b": -2, "operator": "●", "correct_answer": 5.083709268125845}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 3x, compute -4◆4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "3x", "a": -4, "b": 4, "operator": "◆", "correct_answer": 6.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1x, b●-2 = 13. Find b.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1x", "known_var": "a", "known_value": -2, "target_var": "b", "operator": "●", "result": 13, "correct_answers": [-4.242641, 4.242641]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, b★4 = 9. Find b.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "a", "known_value": 4, "target_var": "b", "operator": "★", "result": 9, "correct_answers": [80.342148]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 2◆4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 2, "b": 4, "operator": "◆", "correct_answer": 6.693147180559945}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, a●5 = 18. Find a.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "b", "known_value": 5, "target_var": "a", "operator": "●", "result": 18, "correct_answers": [3.1e-05]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 3x, compute 3●4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "3x", "a": 3, "b": 4, "operator": "●", "correct_answer": 16.5}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 1●3.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 1, "b": 3, "operator": "●", "correct_answer": 7.530294802468585}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 1★2.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 1, "b": 2, "operator": "★", "correct_answer": 6.956449142415282}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, compute -2★1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^2", "a": -2, "b": 1, "operator": "★", "correct_answer": 9.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 3x, compute -5●4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "3x", "a": -5, "b": 4, "operator": "●", "correct_answer": -7.5}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -1x, a◆-3 = 15. Find a.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "-1x", "known_var": "b", "known_value": -3, "target_var": "a", "operator": "◆", "result": 15, "correct_answers": [-5.196152, 5.196152]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute 4●5.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": 4, "b": 5, "operator": "●", "correct_answer": 98.25}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -4★-2.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -4, "b": -2, "operator": "★", "correct_answer": 5.306852819440055}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 1◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 1, "b": 5, "operator": "◆", "correct_answer": 6.256640120404914}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute -5★3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": -5, "b": 3, "operator": "★", "correct_answer": 22.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute -4●1.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": -4, "b": 1, "operator": "●", "correct_answer": 21.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -3◆-1.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -3, "b": -1, "operator": "◆", "correct_answer": 4.90138771133189}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 2x, b★4 = 11. Find b.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "2x", "known_var": "a", "known_value": 4, "target_var": "b", "operator": "★", "result": 11, "correct_answers": [-4.582576, 4.582576]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 2◆3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 2, "b": 3, "operator": "◆", "correct_answer": 6.573845660053303}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 1★2.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 1, "b": 2, "operator": "★", "correct_answer": 6.956449142415282}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 3x, compute 0●2.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "3x", "a": 0, "b": 2, "operator": "●", "correct_answer": 12.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -1x, compute 0◆1.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-1x", "a": 0, "b": 1, "operator": "◆", "correct_answer": 5.5}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -5◆-3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -5, "b": -3, "operator": "◆", "correct_answer": 5.4891743762340095}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -3◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -3, "b": 5, "operator": "◆", "correct_answer": 4.726345317936328}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -2★-1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -2, "b": -1, "operator": "★", "correct_answer": 6.067826442017785}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 0★5.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 0, "b": 5, "operator": "★", "correct_answer": 5.041075725336862}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 2x, compute -5●0.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "2x", "a": -5, "b": 0, "operator": "●", "correct_answer": -19.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -5★-3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -5, "b": -3, "operator": "★", "correct_answer": 5.4891743762340095}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -2★0.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -2, "b": 0, "operator": "★", "correct_answer": 4.583853163452858}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -1x, compute -3●0.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-1x", "a": -3, "b": 0, "operator": "●", "correct_answer": 10.5}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, b★4 = 3. Find b.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "a", "known_value": 4, "target_var": "b", "operator": "★", "result": 3, "correct_answers": [0.199148]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, a●3 = 14. Find a.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "x^2", "known_var": "b", "known_value": 3, "target_var": "a", "operator": "●", "result": 14, "correct_answers": [1.44225]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -1★2.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -1, "b": 2, "operator": "★", "correct_answer": 7.750768411633578}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -5★2.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -5, "b": 2, "operator": "★", "correct_answer": 5.950373152162543}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 1★3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 1, "b": 3, "operator": "★", "correct_answer": 5.299649023251971}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute 2◆3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": 2, "b": 3, "operator": "◆", "correct_answer": 22.25}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 2x, compute -4★5.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "2x", "a": -4, "b": 5, "operator": "★", "correct_answer": 15.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1x, a◆2 = 5. Find a.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1x", "known_var": "b", "known_value": 2, "target_var": "a", "operator": "◆", "result": 5, "correct_answers": [2.44949, -2.44949]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -4◆3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -4, "b": 3, "operator": "◆", "correct_answer": 6.336348875736833}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, compute 2●5.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^2", "a": 2, "b": 5, "operator": "●", "correct_answer": 45.0}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 2★3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 2, "b": 3, "operator": "★", "correct_answer": 6.573845660053303}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, a●1 = 18. Find a.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "b", "known_value": 1, "target_var": "a", "operator": "●", "result": 18, "correct_answers": [6e-06]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^4, compute -3★0.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^4", "a": -3, "b": 0, "operator": "★", "correct_answer": 54.6}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -5●5.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -5, "b": 5, "operator": "●", "correct_answer": 4.082151450673723}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -5★-3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -5, "b": -3, "operator": "★", "correct_answer": 4.8999557172769945}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), b◆-3 = 7. Find b.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "cos(x)", "known_var": "a", "known_value": -3, "target_var": "b", "operator": "◆", "result": 7, "correct_answers": [1.033079, 2.108514]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 3x, compute -2★1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "3x", "a": -2, "b": 1, "operator": "★", "correct_answer": 1.5}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute 1★4.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": 1, "b": 4, "operator": "★", "correct_answer": 69.75}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute -4◆1.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": -4, "b": 1, "operator": "◆", "correct_answer": -57.75}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -4◆-3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -4, "b": -3, "operator": "◆", "correct_answer": 5.712317927548219}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute 2◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": 2, "b": 5, "operator": "◆", "correct_answer": 158.25}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, compute -5●5.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^2", "a": -5, "b": 5, "operator": "●", "correct_answer": 89.33333333333333}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -5◆-4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -5, "b": -4, "operator": "◆", "correct_answer": 5.797878220644789}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -4★-3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -4, "b": -3, "operator": "★", "correct_answer": 5.102077496632204}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -1◆4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -1, "b": 4, "operator": "◆", "correct_answer": 7.193945926731752}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, b★5 = 12. Find b.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "a", "known_value": 5, "target_var": "b", "operator": "★", "result": 12, "correct_answers": [2017.143967]}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^4, compute 3●4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^4", "a": 3, "b": 4, "operator": "●", "correct_answer": 162.2}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -4●-2.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -4, "b": -2, "operator": "●", "correct_answer": 5.306852819440055}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -3●-2.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -3, "b": -2, "operator": "●", "correct_answer": 5.594534891891835}}
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 1★2.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 1, "b": 2, "operator": "★", "correct_answer": 6.956449142415282}}