messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2(-3sin(1π((1((2x - 3)/(2x + 2)) - 3)/(1((2x - 3)/(2x + 2)))) - 3) - 2) + 3) - 3)/(1(-2(-3sin(1π((1((2x - 3)/(2x + 2)) - 3)/(1((2x - 3)/(2x + 2)))) - 3) - 2) + 3) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 48 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(4(5(5(-2sin(2πx - 1) - 2) - 1)^2 + 5(5(-2sin(2πx - 1) - 2) - 1) - 4)^2 + 5(5(5(-2sin(2πx - 1) - 2) - 1)^2 + 5(5(-2sin(2πx - 1) - 2) - 1) - 4) - 3) + 2)/(-2(4(5(5(-2sin(2πx - 1) - 2) - 1)^2 + 5(5(-2sin(2πx - 1) - 2) - 1) - 4)^2 + 5(5(5(-... | 19 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(2|(-2(-1|(-1|x - 2|) + 1| - 1) - 4) + 2| - 1) + 2)/(1(2|(-2(-1|(-1|x - 2|) + 1| - 1) - 4) + 2| - 1) + 3) where -10 ≤ x ≤ 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(1(2(-5((2x)/(-1x - 2)) - 1)^2 - 4(-5((2x)/(-1x - 2)) - 1) - 4)^2 + 2(2(-5((2x)/(-1x - 2)) - 1)^2 - 4(-5((2x)/(-1x - 2)) - 1) - 4) - 4) + 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) = (-1(3((1(-1|(3sin(1πx - 1) + 2) - 3| + 1) + 2)/(-1(-1|(3sin(1πx - 1) + 2) - 3| + 1)))^2 + 2((1(-1|(3sin(1πx - 1) + 2) - 3| + 1) + 2)/(-1(-1|(3sin(1πx - 1) + 2) - 3| + 1)))) + 1)/(3(3((1(-1|(3sin(1πx - 1) + 2) - 3| + 1) + 2)/(-1(-1|(3sin(1π... | 20 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1|(-3|(1(1cos(3πx + 2) - 2) + 5) - 3|)| - 1) + 2)/(-1(1|(-3|(1(1cos(3πx + 2) - 2) + 5) - 3|)| - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(-5((-3(4(-3sin(1πx + 3) - 2)^2 + 5(-3sin(1πx + 3) - 2) + 1) - 2)/(2(4(-3sin(1πx + 3) - 2)^2 + 5(-3sin(1πx + 3) - 2) + 1) + 2))^2 - 4((-3(4(-3sin(1πx + 3) - 2)^2 + 5(-3sin(1πx + 3) - 2) + 1) - 2)/(2(4(-3sin(1πx + 3) - 2)^2 + 5(-3sin(1πx + 3... | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(-5(-3sin(2π(2|((-1x + 1)/(1x + 3)) - 3| - 1) + 3) + 2) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-3(3(3cos(2π((-3x)/(-3x + 4)) + 2) - 3) + 5)^2 - 5(3(3cos(2π((-3x)/(-3x + 4)) + 2) - 3) + 5) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2π(2(-4(-4((2x + 3)/(1x + 3)) - 1)^2 - 3(-4((2x + 3)/(1x + 3)) - 1) - 1)^2 + 3(-4(-4((2x + 3)/(1x + 3)) - 1)^2 - 3(-4((2x + 3)/(1x + 3)) - 1) - 1) - 3) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 660 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-4((2(-2(-2cos(1πx - 3) - 1)^2 - 3(-2cos(1πx - 3) - 1) + 3) + 1)/(1(-2(-2cos(1πx - 3) - 1)^2 - 3(-2cos(1πx - 3) - 1) + 3)))^2 - 1((2(-2(-2cos(1πx - 3) - 1)^2 - 3(-2cos(1πx - 3) - 1) + 3) + 1)/(1(-2(-2cos(1πx - 3) - 1)^2 - 3(-2cos(1πx - 3) - 1) + 3))) - 2)... | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(5(1(3((-3x + 1)/(1x + 1))^2 + 3((-3x + 1)/(1x + 1)) - 5)^2 + 2(3((-3x + 1)/(1x + 1))^2 + 3((-3x + 1)/(1x + 1)) - 5) - 5) + 1)^2 - 5(5(1(3((-3x + 1)/(1x + 1))^2 + 3((-3x + 1)/(1x + 1)) - 5)^2 + 2(3((-3x + 1)/(1x + 1))^2 + 3((-3x + 1)/(1x + 1)) - 5) - 5) + 1... | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2((-3(1(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2)^2 - 4(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2) + 1))/(1(1(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2)^2 - 4(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2) + 1) + 3)) + 1)/(-1((-3(1(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2)^2 - 4(-3(2|x| - 1)^2 + 2(2|x|... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1(4((-2(-2cos(3πx) - 1) + 2)/(3(-2cos(3πx) - 1) - 1)) + 1)^2 + 5(4((-2(-2cos(3πx) - 1) + 2)/(3(-2cos(3πx) - 1) - 1)) + 1) - 5) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation 2((-2(1|(-3(-1x^2 - 3x + 5)) + 2| - 3) + 3)/(-2(1|(-3(-1x^2 - 3x + 5)) + 2| - 3) - 2)) - 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 -3|(4(-2(1|(-3|x - 2| + 3) + 1| + 2)^2 + 4(1|(-3|x - 2| + 3) + 1| + 2) + 1) + 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 1((-1(-4(2((-1x - 2)/(-2x - 1))^2 - 2((-1x - 2)/(-2x - 1)) - 3) - 5))/(3(-4(2((-1x - 2)/(-2x - 1))^2 - 2((-1x - 2)/(-2x - 1)) - 3) - 5) + 1))^2 - 2((-1(-4(2((-1x - 2)/(-2x - 1))^2 - 2((-1x - 2)/(-2x - 1)) - 3) - 5))/(3(-4(2((-1x - 2)/(-2x - 1))^2 - 2((-1x - 2)/... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(3(-1|(4(-3cos(1πx - 1) + 1)^2 - 4(-3cos(1πx - 1) + 1))| + 2)^2 + 3(-1|(4(-3cos(1πx - 1) + 1)^2 - 4(-3cos(1πx - 1) + 1))| + 2) + 2) - 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 95 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1((-2((-2(-2|(5x^2 - 4x - 3)| - 1) - 3)/(-1(-2|(5x^2 - 4x - 3)| - 1))))/(3((-2(-2|(5x^2 - 4x - 3)| - 1) - 3)/(-1(-2|(5x^2 - 4x - 3)| - 1))) - 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(-3|(-1(2|(-1x^2 - 2x) + 3|)^2 + 3(2|(-1x^2 - 2x) + 3|) - 2) + 1|) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(5(-2(-2sin(2π(-2x) + 1) + 3)^2 + 2(-2sin(2π(-2x) + 1) + 3) + 3) + 5) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(3(5(-3(2|x - 1|) + 3) - 5)^2 - 5(5(-3(2|x - 1|) + 3) - 5) - 4) - 2| - 3 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 -1cos(1π(-2((-1(1|(1x^2 + 4)| - 1) - 1)/(-1(1|(1x^2 + 4)| - 1) + 2)) + 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(2cos(3π(-3|((-1(5x + 5) - 2)/(2(5x + 5) + 1)) - 1| + 2)) + 3)^2 - 4(2cos(3π(-3|((-1(5x + 5) - 2)/(2(5x + 5) + 1)) - 1| + 2)) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "How many solutions does the equation 1|(4(4(1|(2|x - 3|) - 2| - 1) + 1) + 1) + 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1(3(3|(-4x^2 - 5x)| - 1) - 4) + 4) + 3| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -2cos(3π(-1|(-3|(-2(-3|x + 2| + 1)^2 + 1(-3|x + 2| + 1) + 2) + 2| + 2) + 3| - 3)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1224 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-2|((2(3cos(3π(-4x - 3) - 1) + 3) + 2)/(1(3cos(3π(-4x - 3) - 1) + 3) - 3)) - 3| + 3) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many solutions does the equation -3|(3|(4(-5(1x^2 - 1x - 3))^2 - 2(-5(1x^2 - 1x - 3)) - 5) - 3| - 1) - 3| = 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 -2sin(1π(1(-2((3(-1x + 3) + 3)/(2(-1x + 3) - 3)) + 4)^2 - 3) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 242 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2π(4(-4((-2((-3x - 1)/(-2x)) + 2)/(-3((-3x - 1)/(-2x)) + 1))) + 4) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2π(-1|(2|(-2|((1x + 2)/(-1x - 1)) + 3| - 3) + 2| - 3) + 3|) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(2π(5((2((-3(-3|x| + 3) - 1)/(3(-3|x| + 3))) + 2)/(-1((-3(-3|x| + 3) - 1)/(3(-3|x| + 3))) - 3))^2 + 3((2((-3(-3|x| + 3) - 1)/(3(-3|x| + 3))) + 2)/(-1((-3(-3|x| + 3) - 1)/(3(-3|x| + 3))) - 3)) + 1)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the a... | 62 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1((2(-3((-3(2cos(3πx + 1)) - 2)/(-1(2cos(3πx + 1))))^2 + 4((-3(2cos(3πx + 1)) - 2)/(-1(2cos(3πx + 1)))) + 4) + 2)/(-2(-3((-3(2cos(3πx + 1)) - 2)/(-1(2cos(3πx + 1))))^2 + 4((-3(2cos(3πx + 1)) - 2)/(-1(2cos(3πx + 1)))) + 4))) - 5 equals zer... | 64 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3((-1(-3(-5(3cos(3πx + 3) - 1) + 3) - 4) + 2)/(1(-3(-5(3cos(3πx + 3) - 1) + 3) - 4))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(2|(-2|(-3(-2|x - 3| + 3)^2 + 4(-2|x - 3| + 3) - 3) + 2| + 1)|) - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1336 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(3π(-5(1((3(4x^2 - 2x - 1) + 1)/(-2(4x^2 - 2x - 1) - 1))^2 - 1((3(4x^2 - 2x - 1) + 1)/(-2(4x^2 - 2x - 1) - 1)) - 3) + 3)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "How many solutions does the equation 1sin(3π(-3(5(-5((-2x - 3)/(3x + 3))^2 - 5((-2x - 3)/(3x + 3)) - 3) + 5)^2) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 292 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-4(-5((-1(-2cos(1πx + 2) + 3) - 2)/(3(-2cos(1πx + 2) + 3) + 1))^2 + 2) + 4)^2 + 3(-4(-5((-1(-2cos(1πx + 2) + 3) - 2)/(3(-2cos(1πx + 2) + 3) + 1))^2 + 2) + 4) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(5(5(2(-2e^(2x) + 1) + 3)^2 - 5(2(-2e^(2x) + 1) + 3) - 4)) - 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(-2cos(1π(2(3|(1x + 1) - 2| - 3)^2 - 3(3|(1x + 1) - 2| - 3) + 3) + 2)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1495 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(2|(3(4(-2sin(1πx - 2) + 2) - 5) + 2) - 1| - 3) + 2)/(-3(2|(3(4(-2sin(1πx - 2) + 2) - 5) + 2) - 1| - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-4(5(-2(-1x^2 - 3x + 3) - 1) - 4)^2 - 5(5(-2(-1x^2 - 3x + 3) - 1) - 4) + 3) - 3)/(3(-4(5(-2(-1x^2 - 3x + 3) - 1) - 4)^2 - 5(5(-2(-1x^2 - 3x + 3) - 1) - 4) + 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(3(-3(-2(2sin(1πx - 1))^2 + 4(2sin(1πx - 1)) - 1) + 2) + 3)^2 + 1(3(-3(-2(2sin(1πx - 1))^2 + 4(2sin(1πx - 1)) - 1) + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3|(3((-3(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) + 2)/(-1(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) - 3))^2 + 5((-3(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) + 2)/(-1(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) - 3)) - 1) - 2| - 1 ... | 7 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-1(2sin(1π((1(-2|x + 2| - 1) + 2)/(3(-2|x + 2| - 1) - 2))) + 3)^2 + 2(2sin(1π((1(-2|x + 2| - 1) + 2)/(3(-2|x + 2| - 1) - 2))) + 3) + 5)^2 + 2(-1(2sin(1π((1(-2|x + 2| - 1) + 2)/(3(-2|x + 2| - 1) - 2))) + 3)^2 + 2(2sin(1π((1(-2|x + 2| - 1) + 2... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5((-1(3(-1cos(1π(1x^2 - 3x - 1) - 1) + 1) + 1) - 2)/(-3(3(-1cos(1π(1x^2 - 3x - 1) - 1) + 1) + 1) + 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 204 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5((1(3(1|(-3cos(1πx) + 2) + 1| - 1) + 1) - 1)/(1(3(1|(-3cos(1πx) + 2) + 1| - 1) + 1)))^2 + 1((1(3(1|(-3cos(1πx) + 2) + 1| - 1) + 1) - 1)/(1(3(1|(-3cos(1πx) + 2) + 1| - 1) + 1))) - 2 equals zero.\n\nPresent the answer in LaTex format: \\box... | 40 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3|(-2(2(5(3|x - 3| - 2) + 2) - 5) + 5) - 1| - 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|(-1e^(-2(1|((-1((-2x)/(2x - 1)) - 1)/(-1((-2x)/(2x - 1)) + 2)) - 3| - 1))) + 1| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(1π(-3|(1(-4(2|x + 1| + 2)^2 - 2(2|x + 1| + 2) - 3)^2 - 4(-4(2|x + 1| + 2)^2 - 2(2|x + 1| + 2) - 3) - 4)| + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 657 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2π(-2|(-2(-3(-1x - 1)^2 + 2(-1x - 1) - 5) - 4) + 3|)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1419 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(3|(5((1(4x^2 - 1x) - 3)/(-3(4x^2 - 1x) + 1))^2 - 4((1(4x^2 - 1x) - 3)/(-3(4x^2 - 1x) + 1)) - 5) + 2| - 2) - 2 have in the interval [-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((-1(4(-1(1|x + 2| - 2))^2 - 2(-1(1|x + 2| - 2)) - 2) + 3)/(-1(4(-1(1|x + 2| - 2))^2 - 2(-1(1|x + 2| - 2)) - 2) - 3)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -4(-4(2sin(3π(-3(2|x - 2| + 1)^2 + 1(2|x - 2| + 1) - 3) - 2) - 1)^2 + 3(2sin(3π(-3(2|x - 2| + 1)^2 + 1(2|x - 2| + 1) - 3) - 2) - 1) + 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1508 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((1((-3(2cos(1π(-1x^2 + 5) + 2) + 2) - 3)/(-3(2cos(1π(-1x^2 + 5) + 2) + 2) + 2)) - 3)/(1((-3(2cos(1π(-1x^2 + 5) + 2) + 2) - 3)/(-3(2cos(1π(-1x^2 + 5) + 2) + 2) + 2)) + 2))| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed... | 200 | MATH |
[
{
"content": "How many solutions does the equation 4(-3|(-3|(-2sin(1π(-5x - 3) + 2) - 1) + 2| + 3) - 2| + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "How many solutions does the equation -3sin(1π(2(3(5(2|x + 1| + 1)^2 + 4(2|x + 1| + 1) + 4) - 3)^2 + 4(3(5(2|x + 1| + 1)^2 + 4(2|x + 1| + 1) + 4) - 3)) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 219 | MATH |
[
{
"content": "How many solutions does the equation -3|(1((3(-1sin(2π((-2x - 1)/(3x - 2)) + 2) + 1) - 2)/(1(-1sin(2π((-2x - 1)/(3x - 2)) + 2) + 1) + 1))^2 - 3((3(-1sin(2π((-2x - 1)/(3x - 2)) + 2) + 1) - 2)/(1(-1sin(2π((-2x - 1)/(3x - 2)) + 2) + 1) + 1)) + 4) - 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent t... | 58 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(-5(-3((1(2x^2 - 2x) - 2)/(1(2x^2 - 2x)))^2 - 4((1(2x^2 - 2x) - 2)/(1(2x^2 - 2x)))) - 2)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(2π((-2((1(5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 5) + 3)/(-1(5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 5) + 2)) - 1)/(-2((1(5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 5) + 3)/(-1(5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 5) + 2)) - 2)) + 1... | 764 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(-3((-1(1cos(1π(-5x^2 + 4x + 3) - 2) + 1) + 1)/(-1(1cos(1π(-5x^2 + 4x + 3) - 2) + 1) - 1)) - 1) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4((2(3|(2|(1x - 3) - 2| - 1) - 3| - 1) - 3)/(-3(3|(2|(1x - 3) - 2| - 1) - 3| - 1)))^2 + 2 equals zero.\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|(1|((2(-3(1|x - 2| - 2) + 5) - 3)/(2(-3(1|x - 2| - 2) + 5) + 2)) - 3|) - 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(2sin(2π((1(-1(2x + 3)^2 + 1(2x + 3) + 4))/(-2(-1(2x + 3)^2 + 1(2x + 3) + 4) - 2)) - 1) + 1) - 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(3(2sin(3π(3|(-3x + 5)| + 3) - 2)) + 1) + 3)/(2(3(2sin(3π(3|(-3x + 5)| + 3) - 2)) + 1) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 540 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-3cos(1π(4(-1(-2x + 3)^2 + 1(-2x + 3) + 3)) + 1))^2 + 4(-3cos(1π(4(-1(-2x + 3)^2 + 1(-2x + 3) + 3)) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1593 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(5((3(1(-1x^2 + 5x + 4) + 2) + 2)/(2(1(-1x^2 + 5x + 4) + 2) - 1))^2 + 4((3(1(-1x^2 + 5x + 4) + 2) + 2)/(2(1(-1x^2 + 5x + 4) + 2) - 1)) - 2) - 1)/(2(5((3(1(-1x^2 + 5x + 4) + 2) + 2)/(2(1(-1x^2 + 5x + 4) + 2) - 1))^2 + 4((3(1(-1x^2 + 5x + 4) +... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(3π(1(4(-4(4x + 5)^2 - 4(4x + 5) - 4) - 3) + 5) + 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1242 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π(-5((-2(-2|(2x^2 + 4x - 5) - 2| + 2) - 3)/(-2(-2|(2x^2 + 4x - 5) - 2| + 2) + 3)) - 1)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(1π(2|(-1|(4((-3x - 2)/(2x)) + 4)| - 2) - 2| - 1) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(-5(3sin(3π(-3((-3x)/(2x - 1)) + 2) + 2) + 1)^2 + 2(3sin(3π(-3((-3x)/(2x - 1)) + 2) + 2) + 1) + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | MATH |
[
{
"content": "How many solutions does the equation (3(1|((1(1|(1x) + 3| - 1) + 2)/(1(1|(1x) + 3| - 1) + 1)) - 3| - 2) + 2)/(-3(1|((1(1|(1x) + 3| - 1) + 2)/(1(1|(1x) + 3| - 1) + 1)) - 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 solutions does the equation -3(2|(1|(-2sin(2π(3x + 1) - 1) + 1) - 1| - 3) + 1|) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(2(-3((-3(-3sin(3πx + 3)) - 3)/(1(-3sin(3πx + 3)))) + 3) + 4) - 2)/(-2(2(-3((-3(-3sin(3πx + 3)) - 3)/(1(-3sin(3πx + 3)))) + 3) + 4) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-2(1e^(-1((-1(-3x + 3) - 1)/(3(-3x + 3)))) - 3)^2 - 3(1e^(-1((-1(-3x + 3) - 1)/(3(-3x + 3)))) - 3) + 3)^2 - 2(-2(1e^(-1((-1(-3x + 3) - 1)/(3(-3x + 3)))) - 3)^2 - 3(1e^(-1((-1(-3x + 3) - 1)/(3(-3x + 3)))) - 3) + 3) + 3 have in the interval [-10, 10]?\n\nPr... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(2(-3|(-2|(2x^2 + 3x - 1) - 3|) + 3| - 1)^2 + 2(-3|(-2|(2x^2 + 3x - 1) - 3|) + 3| - 1) - 2)^2 - 3(2(-3|(-2|(2x^2 + 3x - 1) - 3|) + 3| - 1)^2 + 2(-3|(-2|(2x^2 + 3x - 1) - 3|) + 3| - 1) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex f... | 16 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-3sin(3π((1(-3(4x^2 + 5x) - 1) + 1)/(-3(-3(4x^2 + 5x) - 1) + 4)) + 3) + 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "How many solutions does the equation (-2(-2cos(1π(2((3(-5x - 2) + 3)/(-1(-5x - 2)))^2 + 3((3(-5x - 2) + 3)/(-1(-5x - 2))) + 1) - 2) - 1) - 3)/(-1(-2cos(1π(2((3(-5x - 2) + 3)/(-1(-5x - 2)))^2 + 3((3(-5x - 2) + 3)/(-1(-5x - 2))) + 1) - 2) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the ans... | 83 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(1((-2(1cos(2π((1x + 2)/(-3x - 1))) + 2) - 1)/(3(1cos(2π((1x + 2)/(-3x - 1))) + 2) - 2))^2 - 1)^2 + 5(1((-2(1cos(2π((1x + 2)/(-3x - 1))) + 2) - 1)/(3(1cos(2π((1x + 2)/(-3x - 1))) + 2) - 2))^2 - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer i... | 32 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-1|(2|(-2cos(3π(-5x^2 + 5x + 5)) + 3) + 2| - 3) - 2| - 1) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1453 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4((2(3(5(2sin(3πx - 2) - 1)^2 - 4(2sin(3πx - 2) - 1)) - 2))/(1(3(5(2sin(3πx - 2) - 1)^2 - 4(2sin(3πx - 2) - 1)) - 2) + 1))^2 + 1((2(3(5(2sin(3πx - 2) - 1)^2 - 4(2sin(3πx - 2) - 1)) - 2))/(1(3(5(2sin(3πx - 2) - 1)^2 - 4(2sin(3πx - 2) - 1)) ... | 195 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|((-2((2(-2|(-1x^2 + 5x + 1)| + 1) - 1)/(2(-2|(-1x^2 + 5x + 1)| + 1) - 3)) - 1)/(2((2(-2|(-1x^2 + 5x + 1)| + 1) - 1)/(2(-2|(-1x^2 + 5x + 1)| + 1) - 3)) - 1))| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(3cos(3π(1(-2|(-4x + 3)| - 1) - 5) - 1) - 2) + 2)/(3(3cos(3π(1(-2|(-4x + 3)| - 1) - 5) - 1) - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 237 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1((1(-3(2cos(3π(-1|x + 1| - 1) + 1) + 2) + 1) + 2)/(-2(-3(2cos(3π(-1|x + 1| - 1) + 1) + 2) + 1) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1(-3sin(3π(4(3|x + 2| - 2) + 2) + 1) - 1)^2 + 4(-3sin(3π(4(3|x + 2| - 2) + 2) + 1) - 1) - 5)^2 - 5(1(-3sin(3π(4(3|x + 2| - 2) + 2) + 1) - 1)^2 + 4(-3sin(3π(4(3|x + 2| - 2) + 2) + 1) - 1) - 5) equals zero.\n\nPresent the answer in LaTex f... | 369 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(1π(-3(-3(-2|((-3x - 3)/(-3x + 1)) + 1| - 2)^2 - 1(-2|((-3x - 3)/(-3x + 1)) + 1| - 2) - 4) - 1) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 332 | MATH |
[
{
"content": "How many solutions does the equation -1(3|(1(-1|(-3x^2 + 3x - 1) - 1| + 1)^2 + 5(-1|(-3x^2 + 3x - 1) - 1| + 1) - 1) - 2|)^2 - 2(3|(1(-1|(-3x^2 + 3x - 1) - 1| + 1)^2 + 5(-1|(-3x^2 + 3x - 1) - 1| + 1) - 1) - 2|) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(-4(4(-1((-1x + 3)/(-3x + 4)) - 4)^2 + 4(-1((-1x + 3)/(-3x + 4)) - 4) + 2)^2 + 5(4(-1((-1x + 3)/(-3x + 4)) - 4)^2 + 4(-1((-1x + 3)/(-3x + 4)) - 4) + 2) + 2)^2 - 4(-4(4(-1((-1x + 3)/(-3x + 4)) - 4)^2 + 4(-1((-1x + 3)/(-3x + 4)) - 4) + 2)^2 + 5(4(-1((-1x + 3)... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π(1(2|(-2|(1|x - 3| + 3) - 1| - 2) - 1| - 1) + 2)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2((2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 2)/(2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 1))^2 + 4((2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 2)/(2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 1)) - 2)^2 + 2(2((2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 2)/(2((-2(-... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(-3((-3(-3cos(1π(-1x^2 - 3x - 2) + 3) - 1) - 3)/(3(-3cos(1π(-1x^2 - 3x - 2) + 3) - 1) + 2))^2 + 1((-3(-3cos(1π(-1x^2 - 3x - 2) + 3) - 1) - 3)/(3(-3cos(1π(-1x^2 - 3x - 2) + 3) - 1) + 2)) + 5) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex... | 325 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-1(2(3cos(3π(-1|x - 1| + 1) + 3))^2 - 4)^2 + 1(2(3cos(3π(-1|x - 1| + 1) + 3))^2 - 4) + 1)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(-3(1(4(2cos(3πx - 2) + 2) - 4)^2 - 5(4(2cos(3πx - 2) + 2) - 4) - 2)^2 - 1(1(4(2cos(3πx - 2) + 2) - 4)^2 - 5(4(2cos(3πx - 2) + 2) - 4) - 2) + 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 200 | MATH |
[
{
"content": "How many solutions does the equation -5(-1|(2|(2|(5x^2 - 5x - 2) - 1|) + 1| - 2) + 1| + 2)^2 + 3(-1|(2|(2|(5x^2 - 5x - 2) - 1|) + 1| - 2) + 1| + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(1(2sin(3π(-2|(1|x + 3| + 2) - 3| + 2) - 2) + 1)^2 + 3(2sin(3π(-2|(1|x + 3| + 2) - 3| + 2) - 2) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(2π(3(3|((-2(-2|x + 2| - 3) + 1)/(1(-2|x + 2| - 3) + 3)) + 2| - 2)^2 - 4(3|((-2(-2|x + 2| - 3) + 1)/(1(-2|x + 2| - 3) + 3)) + 2| - 2) + 1) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 276 | MATH |
[
{
"content": "How many solutions does the equation 2|(3sin(1π(2|((1(2|x - 3| - 1))/(-1(2|x - 3| - 1) - 1)) + 1| - 1) - 1) + 2) - 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2((2((-2(1|(-4x^2 + 2x + 5) + 2| - 2) - 2)/(3(1|(-4x^2 + 2x + 5) + 2| - 2) + 2)) - 3)/(-3((-2(1|(-4x^2 + 2x + 5) + 2| - 2) - 2)/(3(1|(-4x^2 + 2x + 5) + 2| - 2) + 2)))) - 3)/(-2((2((-2(1|(-4x^2 + 2x + 5) + 2| - 2) - 2)/(3(1|(-4x^2 + 2x + 5... | 4 | MATH |
[
{
"content": "How many solutions does the equation 3|(2sin(3π((-1(-2((-1x - 2)/(3x - 1))^2 + 2((-1x - 2)/(3x - 1)) + 5) + 1)/(-1(-2((-1x - 2)/(3x - 1))^2 + 2((-1x - 2)/(3x - 1)) + 5) - 2)) + 3) + 3) - 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 50 | MATH |
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