prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = \sin{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

g: \sin{\left(x \right)}

problem_type: expression

correct_answer: 2 x + \cos{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \tan{\left(x \right)}
g(x) = e^{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

f: \tan{\left(x \right)}

correct_answer: e^{x} + \tan^{2}{\left(x \right)} + 1


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = e^{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2 e^{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \log{\left(x \right)}
g(x) = x^{3}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

f: \log{\left(x \right)}

correct_answer: 3 x^{2} + \frac{1}{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = \sin{\left(x \right)}

Find the numerical value of f□g at x = 3.1416.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

f: \sin{\left(x \right)}

problem_type: evaluate

correct_answer: -2.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x
g(x) = \tan{\left(x \right)}

Find the numerical value of f□g at x = 0.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

f: x

g: \tan{\left(x \right)}

correct_answer: 2.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x
g(x) = \sqrt{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

g: \sqrt{x}

correct_answer: 1 + \frac{1}{2 \sqrt{x}}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = \cos{\left(x \right)}

Find the numerical value of f□g at x = 3.1416.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

g: \cos{\left(x \right)}

correct_answer: -1.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{3}
g(x) = \sqrt{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 3 x^{2} + \frac{1}{2 \sqrt{x}}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = x^{2}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2 x + e^{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = x^{2}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2 x + \cos{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \log{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

g: \log{\left(x \right)}

correct_answer: e^{x} + \frac{1}{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = \cos{\left(x \right)}

Find the numerical value of f□g at x = 3.1416.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 6.2832


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{3}
g(x) = \sin{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 3 x^{2} + \cos{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \sin{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: e^{x} + \cos{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = \log{\left(x \right)}

Find the numerical value of f□g at x = 4.7124.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 9.637


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \log{\left(x \right)}
g(x) = e^{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: e^{x} + \frac{1}{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \tan{\left(x \right)}
g(x) = x^{3}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 3 x^{2} + \tan^{2}{\left(x \right)} + 1


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \cos{\left(x \right)}
g(x) = x^{2}

Find the numerical value of f□g at x = 0.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

f: \cos{\left(x \right)}

correct_answer: 0.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \tan{\left(x \right)}

Find the numerical value of f□g at x = 0.7854.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 4.1933


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \log{\left(x \right)}
g(x) = e^{x}

Find the numerical value of f□g at x = 0.7854.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 3.4665


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = x^{3}

Find the numerical value of f□g at x = 3.1416.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 35.8922


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = x^{3}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 3 x^{2} + \cos{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = x^{2}

Find the numerical value of f□g at x = 4.7124.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 18.8496


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \log{\left(x \right)}
g(x) = \sqrt{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: \frac{1}{x} + \frac{1}{2 \sqrt{x}}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = e^{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: e^{x} + \cos{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \sqrt{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: e^{x} + \frac{1}{2 \sqrt{x}}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = \tan{\left(x \right)}

Find the numerical value of f□g at x = 2.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 9.7744


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x
g(x) = e^{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: e^{x} + 1


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \tan{\left(x \right)}
g(x) = \tan{\left(x \right)}

Find the numerical value of f□g at x = 0.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = e^{x}

Find the numerical value of f□g at x = 4.7124.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 111.319


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = x^{2}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2 x + e^{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \log{\left(x \right)}
g(x) = x^{3}

Find the numerical value of f□g at x = 2.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 12.5


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x
g(x) = x

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

g: x

correct_answer: 2


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = x

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: \cos{\left(x \right)} + 1


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \log{\left(x \right)}
g(x) = \log{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: \frac{2}{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \cos{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: e^{x} - \sin{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \sin{\left(x \right)}

Find the numerical value of f□g at x = 0.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \cos{\left(x \right)}
g(x) = \sin{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: - \sin{\left(x \right)} + \cos{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \tan{\left(x \right)}
g(x) = x

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: \tan^{2}{\left(x \right)} + 2


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \cos{\left(x \right)}
g(x) = \log{\left(x \right)}

Find the numerical value of f□g at x = 1.5708.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: -0.3634


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \log{\left(x \right)}
g(x) = x^{2}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2 x + \frac{1}{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \cos{\left(x \right)}
g(x) = \sin{\left(x \right)}

Find the numerical value of f□g at x = 0.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 1.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \cos{\left(x \right)}
g(x) = \sqrt{x}

Find the numerical value of f□g at x = 1.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: -0.3415


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = x

Find the numerical value of f□g at x = 3.1416.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 0.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = \cos{\left(x \right)}

Find the numerical value of f□g at x = 0.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 0.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \tan{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: e^{x} + \tan^{2}{\left(x \right)} + 1


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \sqrt{x}

Find the numerical value of f□g at x = 2.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 7.7426


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = \log{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2 x + \frac{1}{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{2}
g(x) = x^{2}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 4 x


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = \tan{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{3}
g(x) = \tan{\left(x \right)}

Find the numerical value of f□g at x = 2.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 17.7744


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = e^{x}

Find the numerical value of f□g at x = 0.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 2.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sin{\left(x \right)}
g(x) = \sqrt{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: \cos{\left(x \right)} + \frac{1}{2 \sqrt{x}}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{3}
g(x) = x

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 3 x^{2} + 1


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \log{\left(x \right)}
g(x) = x

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 1 + \frac{1}{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sqrt{x}
g(x) = \tan{\left(x \right)}

Find the numerical value of f□g at x = 3.1416.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

f: \sqrt{x}

correct_answer: 1.2821


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{3}
g(x) = e^{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 3 x^{2} + e^{x}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = e^{x}
g(x) = \sqrt{x}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: e^{x} + \frac{1}{2 \sqrt{x}}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \sqrt{x}
g(x) = \cos{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: - \sin{\left(x \right)} + \frac{1}{2 \sqrt{x}}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x^{3}
g(x) = x^{3}

Find the numerical value of f□g at x = 3.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 54.0


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x
g(x) = \sin{\left(x \right)}

Find the numerical value of f□g at x = 3.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 0.01


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = x
g(x) = \cos{\left(x \right)}

Compute the expression for f□g.
Present your answer in LaTeX within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 1 - \sin{\left(x \right)}


prompt:
You are a calculus expert. Solve the problem using the following rules:
The operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.

Given:
f(x) = \cos{\left(x \right)}
g(x) = x^{3}

Find the numerical value of f□g at x = 2.
Provide a single number within [[ ]].
Example: [[2x + \cos(x)]] or [[3.14]]

correct_answer: 11.0907