prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \sin{\left(2 x \right)}
g(x) = 3 \cos{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -2.96
Provide a numerical value rounded to 5 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 3 \sin{\left(2 x \right)}

g_latex: 3 \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + x + 3
g(x) = \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.57
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: \log{\left(e x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \sin{\left(2 x \right)}
g(x) = 2 \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \log{\left(e x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{3 x}
g(x) = 3 \sin{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.11
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = \sin{\left(x \right)}
g(x) = 3 x^{2} + 3 x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

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

expected_str: \sin{\left(x \right)} + 6


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{2 x}
g(x) = 3 \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(x e^{3} \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(x \right)}
g(x) = 3 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -0.15
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \cos{\left(x \right)}

g_latex: 3 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 3 x + 1
g(x) = \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = \cos{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \cos{\left(2 x \right)}

expected_str: 3 e^{2 x} - 4 \cos{\left(2 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = \cos{\left(x \right)}
g(x) = 2 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

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

g_latex: 2 \log{\left(100 x \right)}

expected_str: \cos{\left(x \right)} - \frac{2}{x^{2}}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = 3 \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.54
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(1000 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 3 x + 1
g(x) = 3 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.23
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(10 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 3 x + 3
g(x) = 3 \sin{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 2.72
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \sin{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(3 x \right)}
g(x) = 2 \cos{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.2
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \cos{\left(3 x \right)}

g_latex: 2 \cos{\left(2 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{x}
g(x) = \sin{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

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

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


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{2 x}
g(x) = 3 \cos{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \cos{\left(2 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(2 x \right)}
g(x) = 2 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \sin{\left(2 x \right)}

g_latex: 2 \log{\left(10 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + x + 1
g(x) = \cos{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \sin{\left(2 x \right)}
g(x) = 2 \sin{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \sin{\left(x \right)}

expected_str: 2 \left(3 \cos{\left(x \right)} - 1\right) \sin{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = \cos{\left(2 x \right)}
g(x) = x^{2} + 3 x + 1
Compute: f▽g = f(x) + g''(x)
at x = 0.29
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: \cos{\left(2 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{x}
g(x) = x^{2} + 2 x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = 2 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.14
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(3 x \right)}
g(x) = 3 x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
at x = -2.85
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + x + 1
g(x) = \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \log{\left(1000 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{x}
g(x) = x^{2} + 3 x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \cos{\left(2 x \right)}
g(x) = \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.6
Provide a numerical value rounded to 5 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 3 \cos{\left(2 x \right)}

g_latex: \log{\left(x e^{3} \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{2 x}
g(x) = 2 \sin{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 2.75
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \sin{\left(2 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{3 x}
g(x) = 3 \sin{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 2.31
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 3
g(x) = 3 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{3 x}
g(x) = 2 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: 3 e^{3 x} - 2 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \sin{\left(3 x \right)}
g(x) = 2 x^{2} + 3 x + 2
Compute: f▽g = f(x) + g''(x)
at x = -1.92
Provide a numerical value rounded to 5 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 3 \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = 3 x^{2} + x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + x + 1
g(x) = 3 x^{2} + x + 1
Compute: f▽g = f(x) + g''(x)
at x = 1.99
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + x + 1
g(x) = \log{\left(x e^{2} \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \log{\left(x e^{2} \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 1
g(x) = 2 x^{2} + 2 x + 2
Compute: f▽g = f(x) + g''(x)
at x = -1.45
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \sin{\left(3 x \right)}
g(x) = 2 \sin{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -2.51
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{3 x}
g(x) = \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
at x = -0.29
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = 2 x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = 2 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: 2 e^{x} - 2 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{3 x}
g(x) = 2 \sin{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: 2 e^{3 x} - 2 \sin{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{2 x}
g(x) = 3 x^{2} + x + 2
Compute: f▽g = f(x) + g''(x)
at x = 1.65
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + x + 2
g(x) = 2 \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \log{\left(e x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + x + 1
g(x) = \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
at x = -2.31
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(2 x \right)}
g(x) = 3 \sin{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: 2 \sin{\left(2 x \right)} - 27 \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \sin{\left(2 x \right)}
g(x) = 2 x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
at x = 1.53
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{2 x}
g(x) = 3 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.15
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(100 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = 3 \cos{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -0.45
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + 3 x + 2
g(x) = 2 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.13
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = \cos{\left(x \right)}
g(x) = 3 \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.83
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(e x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = \cos{\left(x \right)}
g(x) = \cos{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -0.17
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \cos{\left(3 x \right)}
g(x) = \log{\left(x e^{2} \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

f_latex: 3 \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + x + 3
g(x) = 3 \cos{\left(3 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.58
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \cos{\left(x \right)}
g(x) = x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
at x = 2.6
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 3 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{3 x}
g(x) = \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{3 x}
g(x) = \log{\left(x e^{3} \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(2 x \right)}
g(x) = x^{2} + 3 x + 1
Compute: f▽g = f(x) + g''(x)
at x = 1.31
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{2 x}
g(x) = 2 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: e^{2 x} - 2 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \cos{\left(2 x \right)}
g(x) = 2 x^{2} + 2 x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: 3 \cos{\left(2 x \right)} + 4


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = 2 x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = 3 x^{2} + 2 x + 2
Compute: f▽g = f(x) + g''(x)
at x = -1.66
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{2 x}
g(x) = x^{2} + x + 3
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(x \right)}
g(x) = 2 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 1.21
Provide a numerical value rounded to 5 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: 2 \sin{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = \cos{\left(3 x \right)}
g(x) = 2 x^{2} + 3 x + 3
Compute: f▽g = f(x) + g''(x)
at x = 2.55
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + 3 x + 2
g(x) = 3 \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 2.71
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(1000 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(2 x \right)}
g(x) = 3 \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{x}
g(x) = 3 x^{2} + x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = 2 x^{2} + 3 x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = \sin{\left(x \right)}
g(x) = x^{2} + 3 x + 1
Compute: f▽g = f(x) + g''(x)
at x = 1.08
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = \sin{\left(3 x \right)}
g(x) = \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -0.92
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

f_latex: \sin{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 2 x + 1
g(x) = \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \log{\left(100 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{2 x}
g(x) = x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
at x = 1.93
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 3 x + 2
g(x) = 2 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.6
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \log{\left(100 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = \cos{\left(2 x \right)}
g(x) = x^{2} + 3 x + 1
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

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


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = 2 x^{2} + x + 1
Compute: f▽g = f(x) + g''(x)
at x = 2.82
Provide a numerical value rounded to 5 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(2 x \right)}
g(x) = \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -1.79
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{x}
g(x) = 2 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \log{\left(10 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 1
g(x) = \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 3
g(x) = 3 x^{2} + x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 3 x + 2
g(x) = 3 x^{2} + 3 x + 2
Compute: f▽g = f(x) + g''(x)
at x = -2.75
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 3 x + 1
g(x) = 3 x^{2} + 2 x + 2
Compute: f▽g = f(x) + g''(x)
at x = 1.43
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = x^{2} + 2 x + 3
g(x) = \cos{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = -0.01
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: \cos{\left(2 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{3 x}
g(x) = 2 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 2.25
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = e^{x}
g(x) = 2 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 2 x + 2
g(x) = 3 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.21
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \log{\left(10 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(3 x \right)}
g(x) = x^{2} + x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

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


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \cos{\left(3 x \right)}
g(x) = 3 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \cos{\left(x \right)}
g(x) = 2 \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.56
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 2 \log{\left(1000 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{x}
g(x) = 2 \log{\left(1000 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{3 x}
g(x) = \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: \log{\left(e x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 x^{2} + 3 x + 1
g(x) = 2 x^{2} + 2 x + 2
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = \cos{\left(3 x \right)}
g(x) = 2 \log{\left(10 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 0.16
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + x + 2
g(x) = \log{\left(e x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 1.65
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 e^{x}
g(x) = \sin{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

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

expected_str: 2 e^{x} - \sin{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{2 x}
g(x) = 2 x^{2} + 2 x + 1
Compute: f▽g = f(x) + g''(x)
at x = 2.85
Provide a numerical value rounded to 5 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 e^{3 x}
g(x) = 2 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 \cos{\left(3 x \right)}
g(x) = \cos{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

expected_str: - 4 \cos{\left(2 x \right)} + 3 \cos{\left(3 x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + 3 x + 3
g(x) = 2 \log{\left(100 x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 1.39
Provide a numerical value rounded to 2 decimal places.
Format your answer within double square brackets: [[answer]]


prompt:
Solve the differential operator problem:
Given:
f(x) = 3 x^{2} + x + 3
g(x) = 3 \cos{\left(x \right)}
Compute: f▽g = f(x) + g''(x)
at x = 2.38
Provide a numerical value rounded to 3 decimal places.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \cos{\left(x \right)}


prompt:
Solve the differential operator problem:
Given:
f(x) = 2 \sin{\left(x \right)}
g(x) = 3 \sin{\left(2 x \right)}
Compute: f▽g = f(x) + g''(x)
Provide the result as a LaTeX mathematical expression.
Format your answer within double square brackets: [[answer]]

g_latex: 3 \sin{\left(2 x \right)}

expected_str: 2 \sin{\left(x \right)} - 12 \sin{\left(2 x \right)}