messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many solutions does the equation 4(3e^(1(-1((1(3x^2 - 1x) - 2)/(-2(3x^2 - 1x) - 2))^2 - 5((1(3x^2 - 1x) - 2)/(-2(3x^2 - 1x) - 2)) + 3)) - 2)^2 + 2(3e^(1(-1((1(3x^2 - 1x) - 2)/(-2(3x^2 - 1x) - 2))^2 - 5((1(3x^2 - 1x) - 2)/(-2(3x^2 - 1x) - 2)) + 3)) - 2) = 0 have in the range [-10, 10]?\n\nPrese... | 4 | MATH |
[
{
"content": "How many solutions does the equation -1(1(-4(-1|(-3cos(3πx - 2) - 3) + 3| + 1)^2 + 5(-1|(-3cos(3πx - 2) - 3) + 3| + 1) + 3) - 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 167 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(5(1(-3(1|x + 3| - 3))^2 - 3(-3(1|x + 3| - 3))) + 3)^2 + 4(5(1(-3(1|x + 3| - 3))^2 - 3(-3(1|x + 3| - 3))) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation 2cos(2π((-2(-1|(-1(-3x^2 + 1x + 4)^2 - 5(-3x^2 + 1x + 4) + 5) - 2| + 3) + 2)/(1(-1|(-1(-3x^2 + 1x + 4)^2 - 5(-3x^2 + 1x + 4) + 5) - 2| + 3))) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 72 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(2sin(3π(3(-3|((1x)/(3x + 3))| + 2) - 3) + 2) + 2) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "How many solutions does the equation -1sin(2π((3(-2|(-1((-3x)/(2x - 1))^2 + 5) - 3| + 1) + 3)/(3(-2|(-1((-3x)/(2x - 1))^2 + 5) - 3| + 1) - 2))) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "How many solutions does the equation 2(-5(3sin(2π(-5(2|x - 1| + 3)^2 + 2(2|x - 1| + 3) + 4) - 3) - 1) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1430 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-3(3|(-4((-1x + 1)/(3x - 1))^2 + 2((-1x + 1)/(3x - 1)) + 5)| - 2))^2 - 5(-3(3|(-4((-1x + 1)/(3x - 1))^2 + 2((-1x + 1)/(3x - 1)) + 5)| - 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 6 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-3((-3((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) + 3)/(2((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) - 1)) + 2)/(3((-3((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) + 3)/(2((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2))... | 4 | MATH |
[
{
"content": "How many solutions does the equation -3cos(1π(-3|(-3(-2|(-2x^2 - 4x - 3) + 1| - 2) + 1) - 1| - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1566 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-3|(-1|(-2|(-1sin(3πx - 3)) + 1|) + 1| - 1) + 3| + 2) + 2)/(1(-3|(-1|(-2|(-1sin(3πx - 3)) + 1|) + 1| - 1) + 3| + 2) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5((1(-2|((-2(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1) - 3)) - 2| + 2) - 3)/(-3(-2|((-2(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1) - 3)) - 2| + 2) + 1))^2 - 2((1(-2|((-2(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1) - 3)) - 2| + 2) - 3)/(-3(-2|((-2(-2|x... | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-1(-1(-2sin(2π((2x + 1)/(-1x + 2)) + 1) - 1)^2 + 5(-2sin(2π((2x + 1)/(-1x + 2)) + 1) - 1) - 5)^2 - 1(-1(-2sin(2π((2x + 1)/(-1x + 2)) + 1) - 1)^2 + 5(-2sin(2π((2x + 1)/(-1x + 2)) + 1) - 1) - 5) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer... | 77 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-2(-1sin(1π(1((-1x - 1)/(2x))^2 + 4((-1x - 1)/(2x)) + 5) + 3) + 2) + 1)^2 + 3(-2(-1sin(1π(1((-1x - 1)/(2x))^2 + 4((-1x - 1)/(2x)) + 5) + 3) + 2) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 55 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(1π(3(-5(-1(-4x - 2) - 2))^2 + 2(-5(-1(-4x - 2) - 2)) - 3) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1298 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-2|(2|((-3(-2x^2 - 2x - 2) + 2)/(-2(-2x^2 - 2x - 2) - 3)) - 2| - 2) - 2|)^2 - 4(-2|(2|((-3(-2x^2 - 2x - 2) + 2)/(-2(-2x^2 - 2x - 2) - 3)) - 2| - 2) - 2|) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4((2(-3sin(2π(1(-4x - 2)^2 + 2(-4x - 2) + 5))) + 1)/(3(-3sin(2π(1(-4x - 2)^2 + 2(-4x - 2) + 5))))) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 141 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(2(2(2(-3cos(2πx - 1) + 1) - 2)^2 - 4(2(-3cos(2πx - 1) + 1) - 2) - 1) - 5) + 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(3cos(3π(-5(2(-5x^2 + 1) - 2)^2 - 2(2(-5x^2 + 1) - 2) - 5)) - 1)^2 + 5(3cos(3π(-5(2(-5x^2 + 1) - 2)^2 - 2(2(-5x^2 + 1) - 2) - 5)) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 258 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-2((-3(1(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1)) - 2)/(2(1(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1)) - 1)) + 1)/(1((-3(1(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1)) - 2)/(2(1(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1)) - 1)) - 2)) + 1 equals zero.\n\nPresent... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(2π(-3|(2(-5(-2|x| + 3)^2 + 1(-2|x| + 3) - 4) + 5) + 2| + 2) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1578 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(3π(1|(-1|((-2(-3|x + 1| - 1) - 2)/(1(-3|x + 1| - 1) + 2)) + 3| - 2) + 3| + 1) + 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(1(2(-3((-2x - 2)/(-3x + 2))^2 - 1((-2x - 2)/(-3x + 2)) - 1)^2 - 2(-3((-2x - 2)/(-3x + 2))^2 - 1((-2x - 2)/(-3x + 2)) - 1) - 4)^2 + 2(2(-3((-2x - 2)/(-3x + 2))^2 - 1((-2x - 2)/(-3x + 2)) - 1)^2 - 2(-3((-2x - 2)/(-3x + 2))^2 - 1((-2x - 2... | 621 | MATH |
[
{
"content": "How many solutions does the equation 2cos(2π(-4(-1((-3(-3x + 1) + 1)/(1(-3x + 1) - 3))^2 - 4((-3(-3x + 1) + 1)/(1(-3x + 1) - 3)) + 2) + 1) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 257 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(-1(3(-2(-2x^2 - 3x - 4))^2 - 5(-2(-2x^2 - 3x - 4)) - 5)^2 - 5(3(-2(-2x^2 - 3x - 4))^2 - 5(-2(-2x^2 - 3x - 4)) - 5) - 4) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 151 | MATH |
[
{
"content": "How many solutions does the equation -1(-2(-2(-1(-3cos(1πx + 2) + 3) + 2) - 3)^2 + 5) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -5(-1|(1|((3(-5x^2 - 2x - 1) + 1)/(-3(-5x^2 - 2x - 1) - 3)) + 3|) - 2| + 3) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 2|((3(-3cos(2π((1((-2x + 2)/(-2x)) - 3)/(-1((-2x + 2)/(-2x)) - 2)) - 1) - 2) + 2)/(2(-3cos(2π((1((-2x + 2)/(-2x)) - 3)/(-1((-2x + 2)/(-2x)) - 2)) - 1) - 2))) + 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 7 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(-1|(1|(-1|(3x - 1) - 2| + 1) + 3| - 3)| + 2)^2 + 2(-1|(1|(-1|(3x - 1) - 2| + 1) + 3| - 3)| + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many solutions does the equation -1((-3(2(3sin(1π(-3|x + 1| + 2) - 3) - 2)^2 + 5(3sin(1π(-3|x + 1| + 2) - 3) - 2) + 2) - 3)/(-2(2(3sin(1π(-3|x + 1| + 2) - 3) - 2)^2 + 5(3sin(1π(-3|x + 1| + 2) - 3) - 2) + 2) - 1))^2 + 4((-3(2(3sin(1π(-3|x + 1| + 2) - 3) - 2)^2 + 5(3sin(1π(-3|x + 1| + 2) - 3) - ... | 246 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2|((3(-3(2x - 2)^2 - 5(2x - 2) - 1) + 2)/(-1(-3(2x - 2)^2 - 5(2x - 2) - 1) - 3)) - 3| + 1) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(1|((-2(3|(2x + 5) - 1| - 2) + 1)/(-3(3|(2x + 5) - 1| - 2) - 1)) - 1| - 1) - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(1(4(2cos(3π((1x - 2)/(3x)) + 2) - 2)^2 - 1(2cos(3π((1x - 2)/(3x)) + 2) - 2) - 1) - 4)^2 + 1(1(4(2cos(3π((1x - 2)/(3x)) + 2) - 2)^2 - 1(2cos(3π((1x - 2)/(3x)) + 2) - 2) - 1) - 4) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format:... | 15 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-1|(-2|((1(-2|x - 1| + 2) - 1)/(3(-2|x - 1| + 2) - 2)) + 1|) + 3| + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(3(-3sin(1π((-2x + 2)/(-1x - 2)) + 1) + 3) - 3) + 4) - 1| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π((-3(3|(2(4x + 1)^2 + 3(4x + 1) - 3)| - 1) + 2)/(2(3|(2(4x + 1)^2 + 3(4x + 1) - 3)| - 1) + 3))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many solutions does the equation -3|(2sin(3π(-1|(-1(-2x - 4)^2 + 3(-2x - 4))| + 2) + 2) + 3) - 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1219 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|((-1((-2(2(2cos(3πx - 1) + 1)^2 - 1(2cos(3πx - 1) + 1) - 4) - 3)/(3(2(2cos(3πx - 1) + 1)^2 - 1(2cos(3πx - 1) + 1) - 4) + 3)))/(1((-2(2(2cos(3πx - 1) + 1)^2 - 1(2cos(3πx - 1) + 1) - 4) - 3)/(3(2(2cos(3πx - 1) + 1)^2 - 1(2cos(3πx - 1) + 1) - 4... | 143 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(3sin(3π(-5(-3(3|x| - 3)^2 - 1(3|x| - 3) - 1)^2 - 2(-3(3|x| - 3)^2 - 1(3|x| - 3) - 1) + 5) - 2) - 3) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 356 | MATH |
[
{
"content": "How many solutions does the equation -1|((-3(3(1((-3x + 1)/(2x + 2))^2 - 5((-3x + 1)/(2x + 2)) - 5)^2 + 4(1((-3x + 1)/(2x + 2))^2 - 5((-3x + 1)/(2x + 2)) - 5) - 3) + 2)/(1(3(1((-3x + 1)/(2x + 2))^2 - 5((-3x + 1)/(2x + 2)) - 5)^2 + 4(1((-3x + 1)/(2x + 2))^2 - 5((-3x + 1)/(2x + 2)) - 5) - 3) + 3)) -... | 6 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-2|(4(-2|(-3|x - 3| - 2) + 3| + 3)^2 - 3(-2|(-3|x - 3| - 2) + 3| + 3) - 3)| + 3) - 1)/(-3(-2|(4(-2|(-3|x - 3| - 2) + 3| + 3)^2 - 3(-2|(-3|x - 3| - 2) + 3| + 3) - 3)| + 3) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\bo... | 12 | MATH |
[
{
"content": "How many solutions does the equation 1|(2(-5(1(-2cos(3πx + 1) - 2)^2 - 3) - 2)) + 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -5(-1(-3(-4(1|x| - 3) - 4)^2 - 4(-4(1|x| - 3) - 4) - 3) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(4(1(3(-1x^2 - 5x - 2)^2 - 4(-1x^2 - 5x - 2) + 1) - 1) + 1)^2 - 5(4(1(3(-1x^2 - 5x - 2)^2 - 4(-1x^2 - 5x - 2) + 1) - 1) + 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(3|((-1(3|(-2|x - 2| - 1) + 3| - 3) + 3)/(3(3|(-2|x - 2| - 1) + 3| - 3) - 2)) + 1|))/(-3(3|((-1(3|(-2|x - 2| - 1) + 3| - 3) + 3)/(3(3|(-2|x - 2| - 1) + 3| - 3) - 2)) + 1|) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\bo... | 4 | MATH |
[
{
"content": "How many solutions does the equation -5(-4(-1|((-2(-3x - 3))/(3(-3x - 3) - 2)) - 2| + 2)^2 + 5(-1|((-2(-3x - 3))/(3(-3x - 3) - 2)) - 2| + 2) + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-5((1((-3(3x) + 3)/(-2(3x))) + 3)/(-2((-3(3x) + 3)/(-2(3x))) - 2))^2 + 4)^2 - 2(-5((1((-3(3x) + 3)/(-2(3x))) + 3)/(-2((-3(3x) + 3)/(-2(3x))) - 2))^2 + 4) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-3(-2sin(1π(3((1(5x + 2) - 1)/(-1(5x + 2) + 3)) + 4) - 1) - 1) - 2)/(1(-2sin(1π(3((1(5x + 2) - 1)/(-1(5x + 2) + 3)) + 4) - 1) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-4(-4(-3(1x^2 + 1x - 5)^2 - 1(1x^2 + 1x - 5) + 5) + 1)^2 - 2(-4(-3(1x^2 + 1x - 5)^2 - 1(1x^2 + 1x - 5) + 5) + 1) + 4)^2 - 1(-4(-4(-3(1x^2 + 1x - 5)^2 - 1(1x^2 + 1x - 5) + 5) + 1)^2 - 2(-4(-3(1x^2 + 1x - 5)^2 - 1(1x^2 + 1x - 5) + 5) + 1) + 4... | 13 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(-3(2cos(1π(-1(-1x - 3) + 3) + 1))^2 + 5(2cos(1π(-1(-1x - 3) + 3) + 1)) - 1) + 3| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|((3(1((1(4x^2 + 4x - 3) - 1)/(1(4x^2 + 4x - 3))) - 5) - 1)/(1(1((1(4x^2 + 4x - 3) - 1)/(1(4x^2 + 4x - 3))) - 5) + 2))| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(2((1(3|(1x - 5)| - 3) + 2)/(3(3|(1x - 5)| - 3) - 2)) - 1) - 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2π(1|(1|((-3(3|x| + 3) + 3)/(1(3|x| + 3) - 3)) + 1| - 3)| - 3) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1|((2(-4(2sin(1πx + 2) - 1) - 3) + 1)/(-1(-4(2sin(1πx + 2) - 1) - 3))) - 3| + 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1|((-1((1(-3sin(2π(-1x - 3) - 2) - 1) + 3)/(-1(-3sin(2π(-1x - 3) - 2) - 1) + 2)) - 3)/(3((1(-3sin(2π(-1x - 3) - 2) - 1) + 3)/(-1(-3sin(2π(-1x - 3) - 2) - 1) + 2)) - 2)) + 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your... | 28 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(1π(-4(1(-1(-2|x + 3| - 3) - 4) - 4)^2 + 2(1(-1(-2|x + 3| - 3) - 4) - 4) + 2) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1252 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(-2|(4(-1(-1|x - 2| + 1)^2 + 2(-1|x - 2| + 1) + 2) - 2) + 2| + 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-3|((-3(-5((2x - 2)/(1x + 2))^2 + 1((2x - 2)/(1x + 2)) + 5) + 3)/(-2(-5((2x - 2)/(1x + 2))^2 + 1((2x - 2)/(1x + 2)) + 5) - 2)) + 2| + 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-1sin(3π((1((-2(1|x - 1| + 3) + 1)/(3(1|x - 1| + 3) + 1)) - 3)/(3((-2(1|x - 1| + 3) + 1)/(3(1|x - 1| + 3) + 1)) + 1)) - 2) + 2)^2 - 3(-1sin(3π((1((-2(1|x - 1| + 3) + 1)/(3(1|x - 1| + 3) + 1)) - 3)/(3((-2(1|x - 1| + 3) + 1)/(3(1|x - 1| + 3) +... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(-5(1|(-1|(-1x^2 + 3x + 5) + 2| + 2) - 1| - 3) + 1)^2 - 3(-5(1|(-1|(-1x^2 + 3x + 5) + 2| + 2) - 1| - 3) + 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation 2(2|((-2(-3cos(1π(-2x) - 1) - 2) + 2)/(2(-3cos(1π(-2x) - 1) - 2) + 1)) + 2| - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -3|((-1(-1e^(1(5(3|x + 1| - 3) + 2)) + 3) - 2)/(1(-1e^(1(5(3|x + 1| - 3) + 2)) + 3) - 3)) - 2| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(2|(4(2(5x^2 - 1x - 4) + 3) + 4) + 3| + 1)^2 + 4(2|(4(2(5x^2 - 1x - 4) + 3) + 4) + 3| + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-1sin(1π(5(3|(-5x + 2) + 1| - 1)) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1499 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3π(1(4(1(4x^2 + 2x + 2)^2 + 3(4x^2 + 2x + 2) + 3) - 2) - 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1059 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(1π(-5((1(1(1|x| + 1) - 1) + 3)/(2(1(1|x| + 1) - 1) + 2))^2 + 3((1(1(1|x| + 1) - 1) + 3)/(2(1(1|x| + 1) - 1) + 2)) - 5) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(2π(2|(-2(-2(2|x + 1| - 3) + 2) + 4) - 1| - 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(1|(1|(-3e^(-2((-2x + 1)/(-1x - 3)))) - 1| - 3) - 2| - 2) + 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((-2(2sin(1π((2(-3x^2 + 3x + 3))/(2(-3x^2 + 3x + 3) - 1)) - 3) + 2))/(-3(2sin(1π((2(-3x^2 + 3x + 3))/(2(-3x^2 + 3x + 3) - 1)) - 3) + 2) + 4)) + 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((-3((-1(-2(-2sin(1πx + 3) + 2)^2 + 5(-2sin(1πx + 3) + 2)) + 2)/(3(-2(-2sin(1πx + 3) + 2)^2 + 5(-2sin(1πx + 3) + 2)) + 3)) - 1)/(1((-1(-2(-2sin(1πx + 3) + 2)^2 + 5(-2sin(1πx + 3) + 2)) + 2)/(3(-2(-2sin(1πx + 3) + 2)^2 + 5(-2sin(1πx + 3)... | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(2|(-1cos(3π(5(1x)^2 + 3(1x) - 2)) + 1) + 2|)^2 + 5(2|(-1cos(3π(5(1x)^2 + 3(1x) - 2)) + 1) + 2|) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1622 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(-5(3|(1(-5x + 4)^2 - 4(-5x + 4) + 5) - 2|) + 5) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1230 | MATH |
[
{
"content": "How many solutions does the equation -1(-1|(-1cos(3π(-2(2x^2 + 1) - 2) - 2) + 3) - 2|)^2 + 3(-1|(-1cos(3π(-2(2x^2 + 1) - 2) - 2) + 3) - 2|) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 978 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-3(3(1sin(2π((3x + 3)/(-2x)) - 3) - 1)^2 - 4(1sin(2π((3x + 3)/(-2x)) - 3) - 1) + 1) + 4) + 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(5(3(1(-4x + 2)^2 + 3(-4x + 2) - 5) + 1)^2 + 1(3(1(-4x + 2)^2 + 3(-4x + 2) - 5) + 1) - 3)^2 - 4(5(3(1(-4x + 2)^2 + 3(-4x + 2) - 5) + 1)^2 + 1(3(1(-4x + 2)^2 + 3(-4x + 2) - 5) + 1) - 3) - 2 equals zero.\n\nPresent the answer in LaTex forma... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1((2(-1sin(1π(3(-4x^2 + 4x) - 3) + 1) - 3) + 2)/(1(-1sin(1π(3(-4x^2 + 4x) - 3) + 1) - 3))) + 1)/(-1((2(-1sin(1π(3(-4x^2 + 4x) - 3) + 1) - 3) + 2)/(1(-1sin(1π(3(-4x^2 + 4x) - 3) + 1) - 3))) + 2) equals zero.\n\nPresent the answer in LaTex... | 946 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(2π(2|(1(1|((3x + 2)/(2x - 1)) - 3| - 1) - 5) - 2| - 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(2sin(1π((-3((2(-5x - 1) + 2)/(1(-5x - 1) - 2)) - 3)/(-1((2(-5x - 1) + 2)/(1(-5x - 1) - 2)) - 2))) + 2)^2 - 1(2sin(1π((-3((2(-5x - 1) + 2)/(1(-5x - 1) - 2)) - 3)/(-1((2(-5x - 1) + 2)/(1(-5x - 1) - 2)) - 2))) + 2) + 1 have in the interval [-10, 10]?\n\nPres... | 17 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(-3sin(3π(3(5(2|x + 2|)^2 + 3(2|x + 2|))^2 - 1(5(2|x + 2|)^2 + 3(2|x + 2|)) + 2) - 2) + 1) + 1)/(-3(-3sin(3π(3(5(2|x + 2|)^2 + 3(2|x + 2|))^2 - 1(5(2|x + 2|)^2 + 3(2|x + 2|)) + 2) - 2) + 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in ... | 115 | MATH |
[
{
"content": "How many solutions does the equation -1(3(1cos(3π(-5(-5x + 3) - 4) - 1) + 1) - 5) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1500 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-4(3((-2(2cos(1πx - 3) - 2) - 2)/(2(2cos(1πx - 3) - 2) - 1)) - 3) + 2) - 3)/(1(-4(3((-2(2cos(1πx - 3) - 2) - 2)/(2(2cos(1πx - 3) - 2) - 1)) - 3) + 2) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 20 | MATH |
[
{
"content": "How many solutions does the equation -1(4(-2(-4(4x^2 + 3x - 3)^2 - 1(4x^2 + 3x - 3) + 5) - 2) + 5)^2 + 5(4(-2(-4(4x^2 + 3x - 3)^2 - 1(4x^2 + 3x - 3) + 5) - 2) + 5) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(5(-2(5(-2|x - 3| - 3) + 1) - 5) + 4) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2000 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2π(2|((2(-2(2|x| - 2)^2 - 4(2|x| - 2) - 4))/(-2(-2(2|x| - 2)^2 - 4(2|x| - 2) - 4) + 3)) + 3| + 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(2sin(1π(3(-3|(-1x^2 - 3x + 3) - 3|)) - 2) + 1) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1133 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(-2(2(-2|(-1x^2 + 3x + 1) - 1| + 3)^2 - 3(-2|(-1x^2 + 3x + 1) - 1| + 3) - 5) - 4)^2 - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (3((3(-2|(-1|((2x - 1)/(-1x + 2))| + 2) - 1| - 1) + 3)/(-1(-2|(-1|((2x - 1)/(-1x + 2))| + 2) - 1| - 1) - 3)) - 2)/(1((3(-2|(-1|((2x - 1)/(-1x + 2))| + 2) - 1| - 1) + 3)/(-1(-2|(-1|((2x - 1)/(-1x + 2))| + 2) - 1| - 1) - 3)) - 2) where -10 ≤ x ≤... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 4(-3cos(3π(-1(-4(1x^2 + 5x + 4)^2 - 5(1x^2 + 5x + 4) - 3)^2 - 4) - 3) - 3)^2 - 5(-3cos(3π(-1(-4(1x^2 + 5x + 4)^2 - 5(1x^2 + 5x + 4) - 3)^2 - 4) - 3) - 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 206 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(2(-1(-3|(4x + 3) - 3| + 1)^2 - 3(-3|(4x + 3) - 3| + 1) - 4)^2 + 4(-1(-3|(4x + 3) - 3| + 1)^2 - 3(-3|(4x + 3) - 3| + 1) - 4) - 1) + 2)/(3(2(-1(-3|(4x + 3) - 3| + 1)^2 - 3(-3|(4x + 3) - 3| + 1) - 4)^2 + 4(-1(-3|(4x + 3) - 3| + 1)^2 - 3(-3|(4x + 3) - 3| + 1... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(-5(-1(-1(-4x + 3) + 2)^2 - 1(-1(-4x + 3) + 2) + 1)^2 - 5(-1(-1(-4x + 3) + 2)^2 - 1(-1(-4x + 3) + 2) + 1) - 1) - 2)/(2(-5(-1(-1(-4x + 3) + 2)^2 - 1(-1(-4x + 3) + 2) + 1)^2 - 5(-1(-1(-4x + 3) + 2)^2 - 1(-1(-4x + 3) + 2) + 1) - 1) - 3) where ... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(3π((-3(3|(-2(-1x^2 - 3x + 4) + 4) + 3| - 2) - 1)/(-1(3|(-2(-1x^2 - 3x + 4) + 4) + 3| - 2) + 3)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 155 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3e^(-1((-1(-2|(5((-2x + 2)/(3x + 3))^2 + 3((-2x + 2)/(3x + 3)) - 2) - 2| + 1) + 1)/(3(-2|(5((-2x + 2)/(3x + 3))^2 + 3((-2x + 2)/(3x + 3)) - 2) - 2| + 1) + 2))) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2π(-1(-2(5((1x)/(2x - 1)) - 3) + 1)^2 + 5(-2(5((1x)/(2x - 1)) - 3) + 1) + 5)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 152 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-3(2sin(3π(-5((3x + 1)/(2x - 1)) + 5) - 3) + 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159 | MATH |
[
{
"content": "How many solutions does the equation 1(2cos(2π(1|(2(-2|x - 1|)^2 - 5(-2|x - 1|) - 5) + 3| - 3) - 2))^2 - 4(2cos(2π(1|(2(-2|x - 1|)^2 - 5(-2|x - 1|) - 5) + 3| - 3) - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1763 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1cos(1π(5(-2|(-3x^2 - 1x + 3) + 1| - 1)^2 - 5(-2|(-3x^2 - 1x + 3) + 1| - 1)) + 3) + 1) + 1)/(2(-1cos(1π(5(-2|(-3x^2 - 1x + 3) + 1| - 1)^2 - 5(-2|(-3x^2 - 1x + 3) + 1| - 1)) + 3) + 1) - 3) equals zero.\n\nPresent the answer in LaTex fo... | 486 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(-2cos(3π(2((3(-1x^2 + 5x - 1) + 2)/(-2(-1x^2 + 5x - 1) + 1)) + 2) - 2)) + 3)/(-2(-2cos(3π(2((3(-1x^2 + 5x - 1) + 2)/(-2(-1x^2 + 5x - 1) + 1)) + 2) - 2)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 90 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-1(5(1(-1x^2 - 5x - 3) - 2)) - 1)^2 - 5(-1(5(1(-1x^2 - 5x - 3) - 2)) - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation (1((-2(-2((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))^2 - 4((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))) + 1)/(2(-2((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))^2 - 4((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))) + 1)) - 2)/(3((-2(-2((3(-1x^2 ... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(-2cos(2π(-2(5(-5x^2 - 1x + 5)^2 - 5(-5x^2 - 1x + 5) - 1)^2 - 2(5(-5x^2 - 1x + 5)^2 - 5(-5x^2 - 1x + 5) - 1) - 2) - 2) + 3) - 1)/(1(-2cos(2π(-2(5(-5x^2 - 1x + 5)^2 - 5(-5x^2 - 1x + 5) - 1)^2 - 2(5(-5x^2 - 1x + 5)^2 - 5(-5x^2 - 1x + 5) - 1) - 2) - 2) + 3)) ... | 142 | MATH |
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