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

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

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

g: x

problem_type: evaluate

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^{3}
g(x) = \sin{\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]]

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

correct_answer: 2.5577


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) = e^{x}

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

f: \sqrt{x}

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) = \log{\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]]

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

problem_type: expression

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

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

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

correct_answer: 1.2929


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]]

f: \sin{\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) = \sin{\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]]

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

correct_answer: \cos{\left(x \right)} + \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) = 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}{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) = \log{\left(x \right)}
g(x) = \sin{\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: 0.2122


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) = \log{\left(x \right)}

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

f: x

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) = x^{3}
g(x) = e^{x}

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: 12.2127


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

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) = \sqrt{x}
g(x) = 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: 1.5642


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) = 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]]

g: \sqrt{x}

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) = \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) = x^{3}
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: 6 x^{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) = x^{2}
g(x) = \tan{\left(x \right)}

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

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

correct_answer: 5.4255


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) = \log{\left(x \right)}
g(x) = \cos{\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: -0.4093


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)}

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

correct_answer: 3.9658


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) = \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: 0.7071


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) = \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) = x^{2}
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: 7.2832


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) = \log{\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: \tan^{2}{\left(x \right)} + 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) = \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{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) = \cos{\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: - \sin{\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) = \cos{\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 - \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) = 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) = x
g(x) = 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: 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^{2}
g(x) = \log{\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: 4.5


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) = \sin{\left(x \right)}
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: 5.3583


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) = \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: \tan^{2}{\left(x \right)} + 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) = 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}{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) = \log{\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: 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) = \tan{\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 + \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^{2}
g(x) = x^{2}

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: 3.1416


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) = \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: 8.0389


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) = \sin{\left(x \right)}

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

correct_answer: 1.0403


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) = e^{x}

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) = x^{2}
g(x) = 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: 10.4248


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}

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: 2.2779


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) = \log{\left(x \right)}
g(x) = \log{\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: 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) = 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) = \sin{\left(x \right)}
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: 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) = \sqrt{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: \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) = 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) = \sin{\left(x \right)}
g(x) = 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: 1.7071


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

Find the numerical value of f□g at x = 1.
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) = \log{\left(x \right)}
g(x) = e^{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: 3.7183


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^{2}

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: 2.5708


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)}

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

correct_answer: 3.5403


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) = 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}{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) = \tan{\left(x \right)}
g(x) = \cos{\left(x \right)}

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

correct_answer: 2.584


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) = \log{\left(x \right)}

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

correct_answer: 4.0


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) = \sqrt{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 + \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) = \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}{\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) = \tan{\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: \tan^{2}{\left(x \right)} + 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) = \log{\left(x \right)}
g(x) = x^{2}

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: 6.6015


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) = x^{2}

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

correct_answer: 4.3536


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) = e^{x}

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^{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
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: 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) = x^{2}
g(x) = 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: 2.5708


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]]

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) = x^{3}
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: 29.609


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) = \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: \cos{\left(x \right)} + \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) = \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: \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^{2}
g(x) = \sin{\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: 2.2779


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) = 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) = \sin{\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: \cos{\left(x \right)} + \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
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: \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) = \sin{\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: 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) = \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) = \sqrt{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]]

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) = \cos{\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 - \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) = \sin{\left(x \right)}
g(x) = x^{2}

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: 2.2779


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}

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

correct_answer: 1.0403


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}

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) = e^{x}
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: 23.1409


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) = \cos{\left(x \right)}
g(x) = e^{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: 1.8768


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}

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

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

correct_answer: 4.4255


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]]

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) = x^{2}
g(x) = x^{2}

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: 3.1416


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

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) = \sqrt{x}
g(x) = e^{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) = 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) = \sin{\left(x \right)}
g(x) = e^{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: 3.2586


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^{2}

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: 7.2832