prompt:
Given f(x) = cos(x), compute 4◆5.
The 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 [[ ]].

problem_type: compute

f: cos(x)

correct_answer: 5.797878220644789


prompt:
Given f(x) = cos(x), compute 1●3.
The 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 [[ ]].

correct_answer: 5.299649023251971


prompt:
Given f(x) = -2x, compute 0●3.
The 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 [[ ]].

correct_answer: -3.0


prompt:
Given f(x) = 1/x, compute 1◆2.
The 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 [[ ]].

correct_answer: 6.693147180559945


prompt:
Given f(x) = x^4, compute -1◆1.
The 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 [[ ]].

correct_answer: 6.4


prompt:
Given f(x) = cos(x), compute -4◆2.
The 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 [[ ]].

correct_answer: 6.1524949315177535


prompt:
Given f(x) = x^3, a◆3 = 16. Find a.
The 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 [[ ]].

problem_type: solve

known_var: b

target_var: a


prompt:
Given f(x) = 1/x, compute -5★-1.
The 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 [[ ]].

correct_answer: 4.3905620875658995


prompt:
Given f(x) = -1x, compute -3★-1.
The 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 [[ ]].

correct_answer: 10.0


prompt:
Given f(x) = sin(x), compute -2●4.
The 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 [[ ]].

f: sin(x)

correct_answer: 6.23749678431647


prompt:
Given f(x) = 1/x, compute -4●-1.
The 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 [[ ]].

correct_answer: 4.613705638880109


prompt:
Given f(x) = x^3, compute -5◆-4.
The 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 [[ ]].

correct_answer: -86.25


prompt:
Given f(x) = 1/x, a◆4 = 5. Find a.
The 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 [[ ]].


prompt:
Given f(x) = 1/x, compute -5◆-1.
The 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 [[ ]].

correct_answer: 4.3905620875658995


prompt:
Given f(x) = 1/x, compute -5◆-4.
The 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 [[ ]].

correct_answer: 5.77685644868579


prompt:
Given f(x) = sin(x), compute 0●1.
The 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 [[ ]].

correct_answer: 6.459697694131861


prompt:
Given f(x) = 2x, a◆-5 = 13. Find a.
The 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 [[ ]].


prompt:
Given f(x) = -2x, b●-4 = 13. Find b.
The 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 [[ ]].

known_var: a

target_var: b


prompt:
Given f(x) = x^2, a★3 = 5. Find a.
The 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 [[ ]].


prompt:
Given f(x) = sin(x), compute -3●0.
The 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 [[ ]].

correct_answer: 4.010007503399555


prompt:
Given f(x) = 1/x, compute -4◆-3.
The 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 [[ ]].

correct_answer: 5.712317927548219


prompt:
Given f(x) = 1/x, compute 4●5.
The 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 [[ ]].

correct_answer: 6.22314355131421


prompt:
Given f(x) = x^3, b●-3 = 11. Find b.
The 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 [[ ]].


prompt:
Given f(x) = 1/x, a●5 = 20. Find a.
The 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 [[ ]].


prompt:
Given f(x) = -1x, compute -3★4.
The 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 [[ ]].

correct_answer: 2.5


prompt:
Given f(x) = 1x, compute -5●-4.
The 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 [[ ]].

correct_answer: 1.5


prompt:
Given f(x) = x^2, a★5 = 19. Find a.
The 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 [[ ]].


prompt:
Given f(x) = sin(x), compute -3◆0.
The 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 [[ ]].

correct_answer: 4.010007503399555


prompt:
Given f(x) = -2x, compute -5◆2.
The 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 [[ ]].

correct_answer: 27.0


prompt:
Given f(x) = -1x, b★-4 = 13. Find b.
The 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 [[ ]].


prompt:
Given f(x) = sin(x), compute -1●1.
The 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 [[ ]].

correct_answer: 6.0


prompt:
Given f(x) = 1/x, compute -3★-1.
The 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 [[ ]].

correct_answer: 4.90138771133189


prompt:
Given f(x) = cos(x), compute 0★3.
The 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 [[ ]].

correct_answer: 6.141120008059867


prompt:
Given f(x) = 2x, compute 2◆5.
The 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 [[ ]].

correct_answer: 27.0


prompt:
Given f(x) = x^2, a◆0 = 12. Find a.
The 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 [[ ]].


prompt:
Given f(x) = cos(x), compute -2●4.
The 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 [[ ]].

correct_answer: 6.1524949315177535


prompt:
Given f(x) = cos(x), compute 3★4.
The 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 [[ ]].

correct_answer: 5.102077496632204


prompt:
Given f(x) = sin(x), compute -1●0.
The 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 [[ ]].

correct_answer: 5.540302305868139


prompt:
Given f(x) = 3x, compute 2★3.
The 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 [[ ]].

correct_answer: 13.5


prompt:
Given f(x) = 1/x, compute -5●-2.
The 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 [[ ]].

correct_answer: 5.083709268125845


prompt:
Given f(x) = 3x, compute -4◆4.
The 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 [[ ]].

correct_answer: 6.0


prompt:
Given f(x) = 1x, b●-2 = 13. Find b.
The 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 [[ ]].


prompt:
Given f(x) = 1/x, b★4 = 9. Find b.
The 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 [[ ]].


prompt:
Given f(x) = 1/x, compute 2◆4.
The 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 [[ ]].

correct_answer: 6.693147180559945


prompt:
Given f(x) = 1/x, a●5 = 18. Find a.
The 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 [[ ]].


prompt:
Given f(x) = 3x, compute 3●4.
The 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 [[ ]].

correct_answer: 16.5


prompt:
Given f(x) = sin(x), compute 1●3.
The 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 [[ ]].

correct_answer: 7.530294802468585


prompt:
Given f(x) = sin(x), compute 1★2.
The 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 [[ ]].

correct_answer: 6.956449142415282


prompt:
Given f(x) = x^2, compute -2★1.
The 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 [[ ]].

correct_answer: 9.0


prompt:
Given f(x) = 3x, compute -5●4.
The 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 [[ ]].

correct_answer: -7.5


prompt:
Given f(x) = -1x, a◆-3 = 15. Find a.
The 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 [[ ]].


prompt:
Given f(x) = x^3, compute 4●5.
The 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 [[ ]].

correct_answer: 98.25


prompt:
Given f(x) = 1/x, compute -4★-2.
The 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 [[ ]].

correct_answer: 5.306852819440055


prompt:
Given f(x) = sin(x), compute 1◆5.
The 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 [[ ]].

correct_answer: 6.256640120404914


prompt:
Given f(x) = -2x, compute -5★3.
The 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 [[ ]].

correct_answer: 22.0


prompt:
Given f(x) = -2x, compute -4●1.
The 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 [[ ]].

correct_answer: 21.0


prompt:
Given f(x) = 1/x, compute -3◆-1.
The 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 [[ ]].

correct_answer: 4.90138771133189


prompt:
Given f(x) = 2x, b★4 = 11. Find b.
The 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 [[ ]].


prompt:
Given f(x) = sin(x), compute 2◆3.
The 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 [[ ]].

correct_answer: 6.573845660053303


prompt:
Given f(x) = sin(x), compute 1★2.
The 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 [[ ]].

correct_answer: 6.956449142415282


prompt:
Given f(x) = 3x, compute 0●2.
The 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 [[ ]].

correct_answer: 12.0


prompt:
Given f(x) = -1x, compute 0◆1.
The 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 [[ ]].

correct_answer: 5.5


prompt:
Given f(x) = 1/x, compute -5◆-3.
The 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 [[ ]].

correct_answer: 5.4891743762340095


prompt:
Given f(x) = sin(x), compute -3◆5.
The 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 [[ ]].

correct_answer: 4.726345317936328


prompt:
Given f(x) = cos(x), compute -2★-1.
The 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 [[ ]].

correct_answer: 6.067826442017785


prompt:
Given f(x) = cos(x), compute 0★5.
The 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 [[ ]].

correct_answer: 5.041075725336862


prompt:
Given f(x) = 2x, compute -5●0.
The 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 [[ ]].

correct_answer: -19.0


prompt:
Given f(x) = 1/x, compute -5★-3.
The 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 [[ ]].

correct_answer: 5.4891743762340095


prompt:
Given f(x) = sin(x), compute -2★0.
The 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 [[ ]].

correct_answer: 4.583853163452858


prompt:
Given f(x) = -1x, compute -3●0.
The 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 [[ ]].

correct_answer: 10.5


prompt:
Given f(x) = 1/x, b★4 = 3. Find b.
The 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 [[ ]].


prompt:
Given f(x) = x^2, a●3 = 14. Find a.
The 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 [[ ]].


prompt:
Given f(x) = cos(x), compute -1★2.
The 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 [[ ]].

correct_answer: 7.750768411633578


prompt:
Given f(x) = cos(x), compute -5★2.
The 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 [[ ]].

correct_answer: 5.950373152162543


prompt:
Given f(x) = cos(x), compute 1★3.
The 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 [[ ]].

correct_answer: 5.299649023251971


prompt:
Given f(x) = x^3, compute 2◆3.
The 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 [[ ]].

correct_answer: 22.25


prompt:
Given f(x) = 2x, compute -4★5.
The 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 [[ ]].

correct_answer: 15.0


prompt:
Given f(x) = 1x, a◆2 = 5. Find a.
The 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 [[ ]].


prompt:
Given f(x) = sin(x), compute -4◆3.
The 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 [[ ]].

correct_answer: 6.336348875736833


prompt:
Given f(x) = x^2, compute 2●5.
The 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 [[ ]].

correct_answer: 45.0


prompt:
Given f(x) = sin(x), compute 2★3.
The 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 [[ ]].

correct_answer: 6.573845660053303


prompt:
Given f(x) = 1/x, a●1 = 18. Find a.
The 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 [[ ]].


prompt:
Given f(x) = x^4, compute -3★0.
The 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 [[ ]].

correct_answer: 54.6


prompt:
Given f(x) = cos(x), compute -5●5.
The 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 [[ ]].

correct_answer: 4.082151450673723


prompt:
Given f(x) = cos(x), compute -5★-3.
The 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 [[ ]].

correct_answer: 4.8999557172769945


prompt:
Given f(x) = cos(x), b◆-3 = 7. Find b.
The 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 [[ ]].


prompt:
Given f(x) = 3x, compute -2★1.
The 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 [[ ]].

correct_answer: 1.5


prompt:
Given f(x) = x^3, compute 1★4.
The 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 [[ ]].

correct_answer: 69.75


prompt:
Given f(x) = x^3, compute -4◆1.
The 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 [[ ]].

correct_answer: -57.75


prompt:
Given f(x) = 1/x, compute -4◆-3.
The 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 [[ ]].

correct_answer: 5.712317927548219


prompt:
Given f(x) = x^3, compute 2◆5.
The 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 [[ ]].

correct_answer: 158.25


prompt:
Given f(x) = x^2, compute -5●5.
The 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 [[ ]].

correct_answer: 89.33333333333333


prompt:
Given f(x) = cos(x), compute -5◆-4.
The 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 [[ ]].

correct_answer: 5.797878220644789


prompt:
Given f(x) = cos(x), compute -4★-3.
The 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 [[ ]].

correct_answer: 5.102077496632204


prompt:
Given f(x) = sin(x), compute -1◆4.
The 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 [[ ]].

correct_answer: 7.193945926731752


prompt:
Given f(x) = 1/x, b★5 = 12. Find b.
The 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 [[ ]].


prompt:
Given f(x) = x^4, compute 3●4.
The 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 [[ ]].

correct_answer: 162.2


prompt:
Given f(x) = 1/x, compute -4●-2.
The 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 [[ ]].

correct_answer: 5.306852819440055


prompt:
Given f(x) = 1/x, compute -3●-2.
The 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 [[ ]].

correct_answer: 5.594534891891835


prompt:
Given f(x) = sin(x), compute 1★2.
The 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 [[ ]].

correct_answer: 6.956449142415282