prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.

solve_var: b


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 14

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 0★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.

type: compute


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 0★1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 1★2

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 1★4

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -5★-2

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -3★-1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -4★-1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 3★6

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 13

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -4★-3

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer a such that a★b = 11

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.

solve_var: a


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -2★2

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -4★2

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer a such that a★b = 7

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -4★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 2

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 12

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -3★0

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 1★2

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 2★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer a such that a★b = 18

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer a such that a★b = 17

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer a such that a★b = 14

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer a such that a★b = 7

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 7★8

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 4★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer a such that a★b = 17

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 3★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -4★-3

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 0★1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 4★10

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 4★7

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer a such that a★b = 18

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 4★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 4★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 0★1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -2★2

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -3★-1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 8

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 0★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 0★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -3★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 20

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 1★5

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Find integer b such that a★b = 7

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute -3★4

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Solve 0★b = b

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.


prompt:
The operation a★b is defined as the definite integral of 2x from a to b.
Mathematically: a★b = ∫ₐᵇ 2x dx = b² - a².

Compute 0★1

Present answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.