data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\sqrt{75x} \\cdot \\sqrt{2x} \\cdot \\sqrt{14x}$ . Express your answer in simplest radical form in terms of $x$."
}
] | math | {
"style": "rule",
"ground_truth": "10x \\sqrt{21x}"
} | {
"index": 5600,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\sqrt{\\sqrt[3]{0.000064}}$. Express your answer as a decimal to the nearest tenth."
}
] | math | {
"style": "rule",
"ground_truth": "0.2"
} | {
"index": 5601,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $\\sum_{n=1}^{2001} n^{3}$."
}
] | math | {
"style": "rule",
"ground_truth": "4012013006001"
} | {
"index": 5602,
"solution": "$\\sum_{n=1}^{2001} n^{3}=\\left(\\sum_{n=1}^{2001} n\\right)^{2}=\\left(\\frac{2001 \\cdot 2002}{2}\\right)^{2}=4012013006001$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $f(x) = 3x^5 + 5x^4 + 6x^3 - 8x^2 + 35x + 12$ using the Horner's Rule when $x = -2$. Find the value of $v_4$."
}
] | math | {
"style": "rule",
"ground_truth": "83"
} | {
"index": 5603,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate $x$ such that the sum \\[1 \\cdot 1979 + 2 \\cdot 1978 + 3 \\cdot 1977 + \\dots + 1978 \\cdot 2 + 1979 \\cdot 1 = 1979 \\cdot 990 \\cdot x.\\]"
}
] | math | {
"style": "rule",
"ground_truth": "661"
} | {
"index": 5604,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate 8 divided by $\\frac{1}{8}.$"
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"index": 5605,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate Mr. $X$'s net gain or loss from the transactions, given that he sells his home valued at $12,000$ to Mr. $Y$ for a $20\\%$ profit and then buys it back from Mr. $Y$ at a $15\\%$ loss."
}
] | math | {
"style": "rule",
"ground_truth": "2160"
} | {
"index": 5606,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\( \\frac{2}{1} \\times \\frac{2}{3} \\times \\frac{4}{3} \\times \\frac{4}{5} \\times \\frac{6}{5} \\times \\frac{6}{7} \\times \\frac{8}{7} \\). Express the answer in decimal form, accurate to two decimal places."
}
] | math | {
"style": "rule",
"ground_truth": "1.67"
} | {
"index": 5607,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\( \\left[6 \\frac{3}{5}-\\left(8.5-\\frac{1}{3}\\right) \\div 3.5\\right] \\times\\left(2 \\frac{5}{18}+\\frac{11}{12}\\right) = \\)"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{368}{27}"
} | {
"index": 5608,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\( t(0) - t(\\pi / 5) + t\\left((\\pi / 5) - t(3 \\pi / 5) + \\ldots + t\\left(\\frac{8 \\pi}{5}\\right) - t(9 \\pi / 5) \\right) \\), where \\( t(x) = \\cos 5x + * \\cos 4x + * \\cos 3x + * \\cos 2x + * \\cos x + * \\). A math student mentioned that he could compute... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 5609,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\(14 \\cdot 31\\) and \\(\\left\\lfloor\\frac{2+\\sqrt{2}}{2}\\right\\rfloor + \\left\\lfloor\\frac{3+\\sqrt{3}}{3}\\right\\rfloor + \\left\\lfloor\\frac{4+\\sqrt{4}}{4}\\right\\rfloor + \\cdots + \\left\\lfloor\\frac{1989+\\sqrt{1989}}{1989}\\right\\rfloor + \\left\... | math | {
"style": "rule",
"ground_truth": "1989"
} | {
"index": 5610,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\(3 \\cdot 15 + 20 \\div 4 + 1\\).\n\nThen add parentheses to the expression so that the result is:\n\n1. The largest possible integer,\n2. The smallest possible integer."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 5611,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\(3^3 \\cdot 4^3\\)."
}
] | math | {
"style": "rule",
"ground_truth": "1728"
} | {
"index": 5612,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\(3^5 \\cdot 6^5\\)."
}
] | math | {
"style": "rule",
"ground_truth": "1,889,568"
} | {
"index": 5613,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\(3^{18} \\div 27^2\\) and multiply the result by 7. Write your answer as an integer."
}
] | math | {
"style": "rule",
"ground_truth": "3720087"
} | {
"index": 5614,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\(7 \\cdot 9\\frac{2}{5}\\)."
}
] | math | {
"style": "rule",
"ground_truth": "65\\frac{4}{5}"
} | {
"index": 5615,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\(\\frac{2}{3} \\cdot \\frac{4}{7} \\cdot \\frac{5}{9} \\cdot \\frac{11}{13}\\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{440}{2457}"
} | {
"index": 5616,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\(\\int_{0}^{1} e^{-x^{2}} \\, dx\\) to an accuracy of 0.001."
}
] | math | {
"style": "rule",
"ground_truth": "0.747"
} | {
"index": 5617,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate \\[\\left|\\left(2 + 2i\\right)^6 + 3\\right|\\]"
}
] | math | {
"style": "rule",
"ground_truth": "515"
} | {
"index": 5618,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate and simplify \n(1) $(1\\frac{1}{2})^0 - (1-0.5^{-2}) \\div \\left(\\frac{27}{8}\\right)^{\\frac{2}{3}}$\n(2) $\\sqrt{2\\sqrt{2\\sqrt{2}}}$"
}
] | math | {
"style": "rule",
"ground_truth": "2^{\\frac{7}{8}}"
} | {
"index": 5619,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate and simplify $\\sqrt[4]{3^5 \\cdot 5^3}$ to the form $c\\sqrt[4]{d}$, where $c$ and $d$ are positive integers. What is $c+d$?"
}
] | math | {
"style": "rule",
"ground_truth": "378"
} | {
"index": 5620,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate both the product and the sum of the least common multiple (LCM) and the greatest common divisor (GCD) of $12$ and $15$."
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"index": 5621,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate how many numbers from 1 to 30030 are not divisible by any of the numbers between 2 and 16."
}
] | math | {
"style": "rule",
"ground_truth": "5760"
} | {
"index": 5622,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the amount of personal income tax (НДФЛ) paid by Sergey over the past year if he is a resident of the Russian Federation and had a stable income of 30,000 rubles per month and a one-time vacation bonus of 20,000 rubles during this period. Last year, Sergey sold his ca... | math | {
"style": "rule",
"ground_truth": "10400"
} | {
"index": 5623,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the angle $\\theta$ for the sum\n\\[e^{3\\pi i/60} + e^{11\\pi i/60} + e^{19\\pi i/60} + e^{27\\pi i/60} + e^{35\\pi i/60} + e^{43\\pi i/60} + e^{51\\pi i/60} + e^{59\\pi i/60}\\]\nwhen expressed in the form of $r e^{i\\theta}$, where $0 \\leq \\theta < 2\\pi$."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{31\\pi}{60}"
} | {
"index": 5624,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the angle \\(\\theta\\) for the expression \\[ e^{11\\pi i/60} + e^{23\\pi i/60} + e^{35\\pi i/60} + e^{47\\pi i/60} + e^{59\\pi i/60} \\] in the form \\( r e^{i \\theta} \\), where \\( 0 \\leq \\theta < 2\\pi \\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7\\pi}{12}"
} | {
"index": 5625,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the arc length of the curve defined by the equation in the rectangular coordinate system.\n\n\\[ y = \\ln 7 - \\ln x, \\sqrt{3} \\leq x \\leq \\sqrt{8} \\]"
}
] | math | {
"style": "rule",
"ground_truth": "1 + \\frac{1}{2} \\ln \\frac{3}{2}"
} | {
"index": 5626,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the arc lengths of curves given by the equations in polar coordinates.\n\n$$\n\\rho = 3 \\varphi, \\quad 0 \\leq \\varphi \\leq \\frac{4}{3}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{10}{3} + \\frac{3}{2} \\ln 3"
} | {
"index": 5627,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the arc lengths of the curves given by equations in the rectangular coordinate system.\n\n$$\ny=1+\\arcsin x-\\sqrt{1-x^{2}}, 0 \\leq x \\leq \\frac{3}{4}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"index": 5628,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the arc lengths of the curves given by the equations in the rectangular coordinate system.\n\n$$\ny=2-e^{x}, \\ln \\sqrt{3} \\leq x \\leq \\ln \\sqrt{8}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "1 + \\frac{1}{2} \\ln \\frac{3}{2}"
} | {
"index": 5629,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the arc lengths of the curves given by the parametric equations.\n\n$$\n\\begin{aligned}\n& \\left\\{\\begin{array}{l}\nx=\\frac{1}{2} \\cos t-\\frac{1}{4} \\cos 2 t \\\\\ny=\\frac{1}{2} \\sin t-\\frac{1}{4} \\sin 2 t\n\\end{array}\\right. \\\\\n& \\frac{\\pi}{2} \\le... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} - 1"
} | {
"index": 5630,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area bounded by the graph of $y = \\arcsin(\\cos x)$ and the $x$-axis over the interval $0 \\leq x \\leq 2\\pi$."
}
] | math | {
"style": "rule",
"ground_truth": "\\pi^2"
} | {
"index": 5631,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of a rectangle which remains unchanged when it is made $3 \\frac{1}{2}$ inches longer and $1 \\frac{1}{3}$ inch narrower, or when it is made $3 \\frac{1}{2}$ inches shorter and $1 \\frac{2}{3}$ inch wider."
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 5632,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of an isosceles triangle if the length of its altitude, drawn to one of the equal sides, is $12 \\mathrm{~cm}$, and the length of the base is $15 \\mathrm{~cm}$."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 5633,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of one petal of the curve $\\rho = \\sin^2 \\varphi$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{16}"
} | {
"index": 5634,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of the crescent moon enclosed by the portion of the circle of radius 4 centered at (0,0) that lies in the first quadrant, the portion of the circle with radius 2 centered at (0,1) that lies in the first quadrant, and the line segment from (0,0) to (4,0)."
}... | math | {
"style": "rule",
"ground_truth": "2\\pi"
} | {
"index": 5635,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of the parallelogram formed by the vectors $\\begin{pmatrix} 4 \\\\ 2 \\\\ -3 \\end{pmatrix}$ and $\\begin{pmatrix} 2 \\\\ -4 \\\\ 5 \\end{pmatrix}$."
}
] | math | {
"style": "rule",
"ground_truth": "6\\sqrt{30}"
} | {
"index": 5636,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of the parallelogram formed by the vectors \\( a \\) and \\( b \\).\n\n$$\n\\begin{aligned}\n& a = p - 4q \\\\\n& b = 3p + q \\\\\n& |p| = 1 \\\\\n& |q| = 2 \\\\\n& \\angle(p, q) = \\frac{\\pi}{6}\n\\end{aligned}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 5637,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of the parallelogram formed by the vectors \\( a \\) and \\( b \\).\n\nGiven:\n\\[ a = 3p - 4q \\]\n\\[ b = p + 3q \\]\n\\[ |p| = 2 \\]\n\\[ |q| = 3 \\]\n\\[ \\text{Angle between } p \\text{ and } q \\text{ is } \\frac{\\pi}{4} \\]"
}
] | math | {
"style": "rule",
"ground_truth": "39\\sqrt{2}"
} | {
"index": 5638,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of the polygon with vertices at $(2,1)$, $(4,3)$, $(6,1)$, $(4,-2)$, and $(3,4)$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11}{2}"
} | {
"index": 5639,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of the shape bounded by the lines given by the equations:\n\n$$\n\\begin{aligned}\n& \\left\\{\\begin{array}{l}\nx=t-\\sin t \\\\\ny=1-\\cos t\n\\end{array}\\right. \\\\\n& y=1 \\quad (0<x<2\\pi, \\, y \\geq 1)\n\\end{aligned}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{2} + 2"
} | {
"index": 5640,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area of the smallest square that can completely contain a circle with a radius of 7 units."
}
] | math | {
"style": "rule",
"ground_truth": "196"
} | {
"index": 5641,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the area, in square units, of the triangle formed by the $x$ and $y$ intercepts of the curve $y = (x-3)^2 (x+2) (x-1)$."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 5642,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the areas of the regions bounded by the curves given in polar coordinates.\n\n$$\nr=\\cos 2 \\phi\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{2}"
} | {
"index": 5643,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the argument of the sum:\n\\[ e^{5\\pi i/36} + e^{11\\pi i/36} + e^{17\\pi i/36} + e^{23\\pi i/36} + e^{29\\pi i/36} \\]\nin the form $r e^{i \\theta}$, where $0 \\le \\theta < 2\\pi$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{17\\pi}{36}"
} | {
"index": 5644,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the arithmetic mean of 17, 29, 45, and 64."
}
] | math | {
"style": "rule",
"ground_truth": "38.75"
} | {
"index": 5645,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the base five product of the numbers $131_5$ and $12_5$."
}
] | math | {
"style": "rule",
"ground_truth": "2122_5"
} | {
"index": 5646,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the car's average miles-per-gallon for the entire trip given that the odometer readings are $34,500, 34,800, 35,250$, and the gas tank was filled with $8, 10, 15$ gallons of gasoline."
}
] | math | {
"style": "rule",
"ground_truth": "22.7"
} | {
"index": 5647,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the circulation of the vector field:\n\na) $\\vec{A}=x^{2} y^{2} \\vec{i}+\\vec{j}+z \\vec{k}$ along the circle $x^{2}+y^{2}=a^{2}, z=0$;\n\nb) $\\dot{A}=(x-2 z) \\dot{i}+(x+3 y+z) \\dot{j}+(5 x+y) \\vec{k}$ along the perimeter of the triangle $A B C$ with vertices $A... | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"index": 5648,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the coefficient of the term containing $x^4$ in the expansion of $(x-1)(x-2)(x-3)(x-4)(x-5)$."
}
] | math | {
"style": "rule",
"ground_truth": "-15"
} | {
"index": 5649,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the corrected average score and variance of a class of 50 students, given that the original average was 70 and the original variance was 102, after two students' scores were corrected from 50 to 80 and from 90 to 60."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 5650,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral\n\n$$\n\\int_{0}^{\\pi / 2} \\frac{\\sin x}{2+\\sin x} \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{2} - \\frac{2 \\pi}{3 \\sqrt{3}}"
} | {
"index": 5651,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{-1}^{0}(x+2)^{3} \\cdot \\ln ^{2}(x+2) \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "4 \\ln^{2} 2 - 2 \\ln 2 + \\frac{15}{32}"
} | {
"index": 5652,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{2 \\pi} \\sin ^{2}\\left(\\frac{x}{4}\\right) \\cos ^{6}\\left(\\frac{x}{4}\\right) d x\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{64}"
} | {
"index": 5653,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{2 \\pi} \\sin ^{4} 3 x \\cos ^{4} 3 x \\, d x\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{64}"
} | {
"index": 5654,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{2 \\pi} \\sin^{6} x \\cos^{2} x \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{64}"
} | {
"index": 5655,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{2 \\sqrt{2}} \\frac{x^{4} \\, dx}{\\left(16-x^{2}\\right) \\sqrt{16-x^{2}}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "20 - 6\\pi"
} | {
"index": 5656,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{2} \\frac{(4 \\sqrt{2-x}-\\sqrt{3 x+2}) d x}{(\\sqrt{3 x+2}+4 \\sqrt{2-x})(3 x+2)^{2}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{32} \\ln 5"
} | {
"index": 5657,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{2} e^{\\sqrt{(2-x) /(2+x)}} \\cdot \\frac{d x}{(2+x) \\sqrt{4-x^{2}}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{e-1}{2}"
} | {
"index": 5658,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{4} e^{\\sqrt{(4-x) /(4+x)}} \\cdot \\frac{d x}{(4+x) \\sqrt{16-x^{2}}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}(e-1)"
} | {
"index": 5659,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\arcsin (3 / \\sqrt{10})} \\frac{2 \\operatorname{tg} x - 5}{(4 \\cos x - \\sin x)^{2}} \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{4} - \\ln 16"
} | {
"index": 5660,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\frac{2\\pi}{3}} \\frac{\\cos^2 x \\, dx}{(1 + \\cos x + \\sin x)^2}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{2} - \\ln 2"
} | {
"index": 5661,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\sin ^{2} x \\, dx}{(1+\\cos x+\\sin x)^{2}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2} - \\frac{1}{2} \\ln 2"
} | {
"index": 5662,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\sin x \\, dx}{(1+\\sin x)^{2}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 5663,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\frac{\\pi}{2}}\\left(x^{2}-5x+6\\right) \\sin 3x \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{67 - 3\\pi}{27}"
} | {
"index": 5664,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi / 4} \\frac{7+3 \\operatorname{tg} x}{(\\sin x+2 \\cos x)^{2}} d x\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "3 \\ln \\left(\\frac{3}{2}\\right) + \\frac{1}{6}"
} | {
"index": 5665,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi} 2^{4} \\cdot \\cos ^{8} x \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{35 \\pi}{8}"
} | {
"index": 5666,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi} 2^{4} \\cdot \\cos ^{8}\\left(\\frac{x}{2}\\right) dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{35\\pi}{8}"
} | {
"index": 5667,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi} 2^{4} \\cdot \\sin ^{6} x \\cos ^{2} x \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{8}"
} | {
"index": 5668,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi} 2^{4} \\cdot \\sin ^{8} x \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{35\\pi}{8}"
} | {
"index": 5669,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi} 2^{4} \\cdot \\sin^{2}\\left(\\frac{x}{2}\\right) \\cos^{6}\\left(\\frac{x}{2}\\right) \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5 \\pi}{8}"
} | {
"index": 5670,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi} 2^{4} \\sin ^{4}\\left(\\frac{x}{2}\\right) \\cos ^{4}\\left(\\frac{x}{2}\\right) d x\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{8}"
} | {
"index": 5671,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\pi}\\left(9 x^{2}+9 x+11\\right) \\cos 3 x \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "-2\\pi - 2"
} | {
"index": 5672,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\sqrt{2} / 2} \\frac{x^{4} \\cdot d x}{\\sqrt{\\left(1-x^{2}\\right)^{3}}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{4} - \\frac{3\\pi}{8}"
} | {
"index": 5673,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{1}^{8} \\frac{5 \\sqrt{x+24}}{(x+24)^{2} \\cdot \\sqrt{x}} \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"index": 5674,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{1}^{e^{2}} \\frac{\\ln ^{2} x}{\\sqrt{x}} \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "24e - 32"
} | {
"index": 5675,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{1}^{e} \\sqrt{x} \\cdot \\ln^{2} x \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{10e\\sqrt{e} - 16}{27}"
} | {
"index": 5676,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{2 \\operatorname{arctg} \\frac{1}{3}}^{2 \\operatorname{arctg} \\frac{1}{2}} \\frac{d x}{\\sin x(1-\\sin x)}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\ln 3 - \\ln 2 + 1"
} | {
"index": 5677,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{6}^{9} \\sqrt{\\frac{9-2x}{2x-21}} \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\pi"
} | {
"index": 5678,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\frac{\\pi}{2}}^{2 \\operatorname{arctg} 2} \\frac{d x}{\\sin ^{2} x(1+\\cos x)}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "29/24"
} | {
"index": 5679,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\frac{\\pi}{2}}^{2 \\operatorname{arctg} 2} \\frac{d x}{\\sin ^{2} x(1-\\cos x)}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "55/96"
} | {
"index": 5680,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\frac{\\pi}{2}}^{2 \\operatorname{arctg} 2} \\frac{d x}{\\sin x(1+\\sin x)}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\ln 2 - \\frac{1}{3}"
} | {
"index": 5681,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\pi / 2}^{2 \\pi} 2^{8} \\cdot \\cos ^{8} x \\, dx\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "105\\pi"
} | {
"index": 5682,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\pi / 4}^{\\arccos (1 / \\sqrt{26})} \\frac{36 \\, dx}{(6 - \\tan x) \\sin 2x}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "6 \\ln 5"
} | {
"index": 5683,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\pi / 4}^{\\arcsin \\sqrt{2 / 3}} \\frac{8 \\tan x \\, dx}{3 \\cos ^{2} x+8 \\sin 2 x-7}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{21} \\ln \\left| \\frac{7\\sqrt{2} - 2}{5} \\right| - \\frac{4}{3} \\ln |2 - \\sqrt{2}|"
} | {
"index": 5684,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n$$\n\\int_{\\pi / 4}^{\\operatorname{arctg} 3} \\frac{d x}{(3 \\operatorname{tg} x+5) \\sin 2 x}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{10} \\ln \\frac{12}{7}"
} | {
"index": 5685,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n\n\\[\n\\int_{0}^{\\frac{\\pi}{4}} \\frac{2 \\cos x + 3 \\sin x}{(2 \\sin x - 3 \\cos x)^{3}} \\, dx\n\\]"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{17}{18}"
} | {
"index": 5686,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the definite integral:\n$$\n\\int_{0}^{\\pi / 4} \\frac{5 \\operatorname{tg} x+2}{2 \\sin 2 x+5} d x\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2} \\ln \\left(\\frac{14}{5}\\right)"
} | {
"index": 5687,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the degree of ionization using the formula:\n\n$$\n\\alpha=\\sqrt{ } K_{\\mathrm{HCN}} \\mathrm{C}\n$$\n\nGiven values:\n\n$$\n\\alpha_{\\text {ion }}=\\sqrt{ }\\left(7,2 \\cdot 10^{-10}\\right) / 0,1=\\sqrt{ } 7,2 \\cdot 10^{-9}=8,5 \\cdot 10^{-5}, \\text{ or } 8,5 \... | math | {
"style": "rule",
"ground_truth": "0.0085"
} | {
"index": 5688,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the difference $(2001 + 2002 + 2003 + \\cdots + 2100) - (51 + 53 + 55 + \\cdots + 149)$."
}
] | math | {
"style": "rule",
"ground_truth": "200050"
} | {
"index": 5689,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the difference between 12.358 and 7.2943, keeping the answer in decimal form."
}
] | math | {
"style": "rule",
"ground_truth": "5.0637"
} | {
"index": 5690,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the difference between the sum of the first 2023 odd counting numbers and the sum of the first 2023 even counting numbers, where even numbers start from 2, and then multiply this difference by 3."
}
] | math | {
"style": "rule",
"ground_truth": "9063"
} | {
"index": 5691,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the distance between the foci of the ellipse defined by the equation\n\\[\\frac{x^2}{36} + \\frac{y^2}{9} = 9.\\]"
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}"
} | {
"index": 5692,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the distance between the points $(5, -3)$ and $(-7, 4)$. Additionally, determine if the points $(5, -3)$, $(-7, 4)$, and $(5, 4)$ form a right triangle."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{193}"
} | {
"index": 5693,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the double integral\n\n$$\n\\iint_{D}\\left(54 x^{2} y^{2}+150 x^{4} y^{4}\\right) d x d y\n$$\n\nwhere the region \\(D\\) is bounded by the lines \\(x=1, y=x^{3}\\), and \\(y=-\\sqrt{x}\\)."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 5694,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the double integrals and change the order of integration.\n\n$$\n\\text{a) } \\int_{0}^{2} dx \\int_{0}^{3}\\left(x^{2} + 2xy\\right) dy\n$$\n\nb) $\\int_{-2}^{0} dy \\int_{0}^{y^{2}}(x+2y) dx$\n\nc) $\\int_{0}^{5} dx \\int_{0}^{5-x} \\sqrt{4 + x + y} dy$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{506}{3}"
} | {
"index": 5695,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the expression $(-2)^4 + (-2)^3 + (-2)^2 + (-2)^1 + 2^1 + 2^2 + 2^3 + 2^4$."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 5696,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the expression $16 \\times 0.5 - (4.5 - 0.125 \\times 8)$.\nA) $4.5$\nB) $4$\nC) $4 \\frac{1}{2}$\nD) $6$\nE) $7$"
}
] | math | {
"style": "rule",
"ground_truth": "4 \\frac{1}{2}"
} | {
"index": 5697,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the expression $200(200-5)-(200\\cdot200-5)$."
}
] | math | {
"style": "rule",
"ground_truth": "-995"
} | {
"index": 5698,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the expression $8 \\times 10^{5}+4 \\times 10^{3}+9 \\times 10+5$."
}
] | math | {
"style": "rule",
"ground_truth": "804095"
} | {
"index": 5699,
"solution": "First, we write out the powers of 10 in full to obtain $8 \\times 100000+4 \\times 1000+9 \\times 10+5$. Simplifying, we obtain $800000+4000+90+5$ or 804095."
} |
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