prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $374,093 |
[
{
"content": "Compute \\( \\iint_S \\mathrm{curl} \\ F \\cdot n \\, dS \\) where \\( S \\) is the portion of the surface \\( z = x^2 + y^2 \\) below \\( z = 16 \\), with \\( n \\) as the downward-pointing normal vector, and \\( F = (z, x, y^2) \\).",
"role": "user"
}
] | -16\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Supplies Expense
Supplies
To record the portion of the supplies expensed during 2014.
Accounts Receivable
Consulting Revenue
To record unbilled revenue worth $850.
Rent Expense
Prepaid Rent
To record rent expense for the month of December 2014.
Depreciation Expense - Equipment
Accumulated Depreciation - Equipment
To record the depreciation expense of equipment for the year 2014. |
[
{
"content": "Andrei wrote 6 consecutive four-digit numbers on the board in ascending order. Under each number, he wrote one of its prime divisors, ensuring all the divisors were different. After erasing the numbers, Boris enters the room. Can Boris always uniquely determine the original numbers from the prime ... | Yes |
[
{
"content": "Compute the residue of the differential form \\( \\frac{dz}{w^3} \\) at the point \\( p \\) on the Riemann surface defined by \\( w^3 = z(z-1)(z-2) \\), where \\( w = 0 \\) and \\( z = 1 \\).",
"role": "user"
}
] | -3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2218.88 L |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 374J |
[
{
"content": "Determine the angle of rotation \\( \\theta \\) of the ellipse given by the equation \\( 3x^2+2xy+3y^2-18x-22y+50=0 \\) with respect to the original axes, such that it transforms to the equation \\( 4x^2+2y^2=1 \\) with respect to a rectangular axes through the point \\((2,3)\\).",
"role": "us... | \dfrac{\pi}{4} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.089 H |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 471 kPa |
[
{
"content": "Find the arc length of the curve $C$ parametrized by \\( \\alpha(t) = (5\\cos t - \\cos 5t, 5\\sin t - \\sin 5t) \\) for \\( t \\in [0, 2\\pi] \\). Use the identities \\( \\cos 4t = \\cos t \\cos 5t + \\sin t \\sin 5t \\) and \\( \\sin^2 t = \\frac{1 - \\cos 2t}{2} \\) to assist in your calculatio... | 40 |
[
{
"content": "What is the ratio of the numerical value of the area, in square units, of an equilateral triangle of side length 4 units to the numerical value of its perimeter, in units? Express your answer as a common fraction in simplest radical form.",
"role": "user"
}
] | \frac{\sqrt{3}}{3} |
[
{
"content": "If $G$ is a nonabelian finite simple group, does $G$ contain a maximal subgroup that is not abelian?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12.81 MGD |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $11,348,967.15 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $68,495,640 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.09 m |
[
{
"content": "If $X$ is a collection of subsets of $\\Omega$ such that $X$ is contained in the $\\sigma$-algebra $\\mathcal{F}$ and $\\mathcal{F}$ is also contained in $X$, does $X$ equal $\\mathcal{F}$?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the minimal solution to the following system of linear congruences:\n\\[ 3x \\equiv 1 \\pmod{8} \\\\\n x \\equiv 7 \\pmod{12} \\\\\n x \\equiv 4 \\pmod{15} \\]",
"role": "user"
}
] | 19 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 724 |
[
{
"content": "In triangle $ABC$, where $AB = 6$, $BC = 10$, and $CA = 8$, let $M$ and $N$ be the midpoints of $BA$ and $BC$, respectively. A point $Y$ is chosen on ray $CM$ such that the circumcircle of triangle $AMY$ is tangent to line $AN$. Determine the area of triangle $NAY$. \\( \\text{(Express your answer... | \dfrac{600}{73} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Kc=[C]^c[D]^d/[A]^a[B]^b |
[
{
"content": "Suppose $f$ is a continuous function such that $f(0) = 0$, $f(1) = 1$, and $f'(x) > 0$ for all $x$ in the interval $[0, 1]$. Given that $\\int_{0}^{1} f(x) \\, dx = \\frac{1}{3}$, find the value of the integral $\\int_{0}^{1} f^{-1}(y) \\, dy$. \\( \\text{Note: } f^{-1} \\text{ denotes the inverse... | \dfrac{2}{3} |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\frac{\\cos x}{4x^2-\\pi^2}dx \\).",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.73e-22 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 21199 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.92x10^-5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.999 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 469e16 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.125 |
[
{
"content": "Given that \\(z_1\\) and \\(z_2\\) are the roots of the equation \\(3z^2 + 3z + b = 0\\), and the points \\(O(0)\\), \\(A(z_1)\\), and \\(B(z_2)\\) form an equilateral triangle, determine the value of \\(b\\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 338.74 nm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.22% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 16.992 nF |
[
{
"content": "Given $r = \\frac{1 + \\sqrt{5}}{2}$, if $x, y, z, w$ are integers satisfying \\((x + yr)(z + wr) = 1\\) and \\(x + yr > 0\\), prove that there exists an integer $k$ such that \\(x + yr = r^k\\).",
"role": "user"
}
] | r^k |
[
{
"content": "A square is drawn such that one of its sides coincides with the line $y = 5$, and so that the endpoints of this side lie on the parabola $y = x^2 + 3x + 2$. What is the area of the square?",
"role": "user"
}
] | 21 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 37.18 N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2d/x^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Z = M * cos(Pitch) * cos(Roll) |
[
{
"content": "Calculate the probability that two random numbers have the same $2$-adic valuation.",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Determine the number of zeros of the polynomial \\( z^7 - 4z^3 + z + 1 = 0 \\) that lie within the interior of the circle \\(|z| = 1\\).",
"role": "user"
}
] | 3 |
[
{
"content": "In a finite $T_1$ topological space, determine the intersection of all open sets containing a point $x$. Provide your answer as a set.",
"role": "user"
}
] | \{x\} |
[
{
"content": "What is the smallest possible value of the correlation \\( \\rho \\) in an \\( n \\times n \\) correlation matrix where the correlation between any pair of two random variables is \\( \\rho \\)?",
"role": "user"
}
] | -\dfrac{1}{n-1} |
[
{
"content": "Find all continuous functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that satisfy the equation \\( f(x+y) + f(x-y) = 2[f(x) + f(y)] \\).",
"role": "user"
}
] | f(x) = ax^2 |
[
{
"content": "Determine the number of real solutions to the equation: $$\\sqrt{3x^2 - 18x + 52} + \\sqrt{2x^2 - 12x + 162} = \\sqrt{-x^2 + 6x + 280}$$",
"role": "user"
}
] | 1 |
[
{
"content": "Consider the sequence \\(g_n\\) defined by \\[g_n=\\prod_{i=1}^n \\left(1+\\frac{X_i}{\\sqrt{i}}\\right)\\] where \\(X_i\\)'s are independent random variables with \\(P(X_i=1)=P(X_i=-1)=0.5\\). Determine whether \\(P(g_n \\rightarrow \\infty)=0\\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.85e-4 s |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\int_0^\\infty nx^2\\sin\\left(\\frac{1}{nx}\\right)dx \\]",
"role": "user"
}
] | \infty |
[
{
"content": "Solve for \\( x \\) in the equation:\n\\[ \\ln x - \\ln(\\sqrt{x}) + \\ln(\\sqrt[4]{x}) - \\ln(\\sqrt[8]{x}) + \\ldots = 2 \\]",
"role": "user"
}
] | e^3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $63.40 |
[
{
"content": "Let the function \\(f(x)= \\sqrt{(x^2-2x+2)(-x^2+3x+10)}-\\sqrt{(-x^{2}+x-1)(x^{2}+x-6)}\\) have a domain \\(D=[a,b+c]\\). Find the value of \\(\\frac{a^3+b^3+c^3}{abc}\\).",
"role": "user"
}
] | 3 |
[
{
"content": "Calculate the residue of the function \\( f(z) = \\frac{z}{1-\\cos(z)} \\) at \\( z=0 \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Calculate the first de Rham cohomology group $H^1_{dR}(S^1)$ of the circle $S^1$.",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 17 mL |
[
{
"content": "Determine the number of integer solutions \\((x, y)\\) to the equation \\((2x + y)^{2} = 2017 + x^{2}\\).",
"role": "user"
}
] | 4 |
[
{
"content": "A baseball league has nine teams. During the season, each of the nine teams plays exactly three games with each of the other teams. What is the total number of games played?",
"role": "user"
}
] | 108 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8 x 10^26 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 490 N/C, pointing downward |
[
{
"content": "Let $T$ be a metric space. A subset of $T$ is regularly open if it is equal to the interior of its closure. Given a proper inclusion $A \\subset B$ of two regularly open sets in $T$, must the difference $B \\setminus A$ have a non-empty interior? Provide a justification for your answer.",
"rol... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 17.76^oC |
[
{
"content": "Determine the value of $x$ such that the series \\[ 2 - \\frac{2^2}{x+1} + \\frac{2^3}{(x+1)^2} - \\frac{2^4}{(x+1)^3} + \\cdots \\] converges to \\( \\frac{9}{5} \\).",
"role": "user"
}
] | 17 |
[
{
"content": "The roots of the polynomial \\( P(x) = x^4 -10x^3 + 35x^2 -51x + 26 \\) form the side lengths of a quadrilateral. The maximum area of such a quadrilateral is of the form \\( \\sqrt{n} \\) for some positive integer \\( n \\). Find \\( n \\).",
"role": "user"
}
] | 21 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.50g |
[
{
"content": "In a group $G$, is it possible for elements $a$, $b$, $c$, and $d$ to satisfy $axb = cxd$ while $ab \\neq cd$? Answer yes or no.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.126 M |
[
{
"content": "Given that \\( \\frac{3 \\pi}{4}<\\theta<\\pi \\) and \\( \\sqrt{2 \\cot \\theta+\\frac{1}{\\sin ^{2} \\theta}}=k-\\cot \\theta \\), find the value of \\( k \\).",
"role": "user"
}
] | -1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Impurities in the sodium bicarbonate and decomposition of the sodium bicarbonate to sodium carbonate can affect the yield and purity of NaCl. Modifications include accounting for known impurities and ensuring the bicarbonate is fresh or stored correctly. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 300 J |
[
{
"content": "In an acute-angled triangle ABC, let $A_2$, $B_2$, and $C_2$ be the midpoints of the altitudes $AA_1$, $BB_1$, and $CC_1$, respectively. Calculate the sum of the angles $\\angle B_2A_1C_2$, $\\angle C_2B_1A_2$, and $\\angle A_2C_1B_2$. \\(\\text{*D. Tereshin*}\\)",
"role": "user"
}
] | 180^\circ |
[
{
"content": "Determine the smallest non-commutative ring with unity, where \"smallest\" refers to having the least cardinality.",
"role": "user"
}
] | 8 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 11854.81 |
[
{
"content": "In the graph $G=(V,E_1\\cup E_2)$, where $T_1=(V,E_1)$ and $T_2=(V,E_2)$ are trees, does there exist a vertex with degree at most 3, even if $E_1\\cap E_2\\neq\\varnothing$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 170 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.71 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 32.21 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 87.8 % |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 11.82 m/s |
[
{
"content": "Determine the value of \\( n \\) such that the following limit holds: \\[ \\lim_{x \\to 1}\\frac{\\frac{\\pi}{4}-\\arctan(x)}{e^{\\sin(\\ln(x))}-x^n} = \\frac{1}{8}. \\] Do not use L'Hôpital's rule or Maclaurin's series expansion.",
"role": "user"
}
] | 5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $10,000 unfavorable |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.75e5 kJ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $2,800 |
[
{
"content": "Given the linear programming problem: Minimize \\(x+y+z-\\alpha t\\) subject to \\(2x - y + z = 6\\), \\(-x + y + t = 3\\), and \\(x, y, z, t \\geq 0\\). If \\((3, 0, 0, \\beta)\\) is an optimal solution, determine the maximum value of \\(\\beta - \\alpha\\).",
"role": "user"
}
] | 7 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.4e+3 V |
[
{
"content": "Calculate the partial derivative of the function \\( f(x,y) = \\begin{cases} 0 & (x,y)=(0,0)\\\\ \\frac{xy}{|x|+|y|} & (x,y) \\neq (0,0) \\end{cases} \\) with respect to \\( x \\) at the point \\( (0,0) \\) using the limit definition.",
"role": "user"
}
] | 0 |
[
{
"content": "Solve the equation: \\( \\sqrt[4]{3(x+5)} - \\sqrt[4]{x+13} = \\sqrt[4]{11-x} - \\sqrt[4]{3(3-x)} \\)",
"role": "user"
}
] | -1 |
[
{
"content": "Let $k, r, n$ be positive integers such that $k+1$ and $r-1$ are relatively prime. Let $N = nk$ and $M = n(n-1)nk/2$. Is it true that the dimension of the vector space $V^{(k,r)}_{N,M}$ is 1 under these conditions?",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The original speed of the first car is 9.9 m/s and the second car is 4.95 m/s. |
[
{
"content": "Evaluate the integral \\( I_n = \\int_0^\\infty \\left(\\operatorname{E}_n(x)e^x - \\frac{1}{1+x}\\right) dx \\) and show that it equals \\(-\\psi(n)\\), where \\(\\operatorname{E}_n\\) denotes the exponential integral and \\(\\psi\\) denotes the polygamma function.",
"role": "user"
}
] | -\psi(n) |
[
{
"content": "How many self-dual Boolean functions are there with 4 variables?",
"role": "user"
}
] | 256 |
[
{
"content": "Determine whether the following inequality holds for all continuous functions $f$ and $g$ on $[0,1]$:\n\\[ \\sup_{x \\in [0,1]} \\left\\{ \\int_{0}^{x} |f(t) - g(t)| \\, dt \\right\\} \\leq \\sup_{x \\in [0,1]} \\left\\{ |f(x) - g(x)| \\right\\}. \\]",
"role": "user"
}
] | Yes |
[
{
"content": "Given that a series $\\sum_{n \\geq 1}a_{n}$ converges, determine if it is always possible to find a subsequence $a_{n_k}$ such that $a_{n_{k+1}} \\geq a_{n_k}$ for all $k \\in \\mathbb{N}$. Answer with 'Yes' or 'No'.",
"role": "user"
}
] | No |
[
{
"content": "Three friends have a total of 6 identical pencils, and each one has at least one pencil. In how many ways can this happen?",
"role": "user"
}
] | 10 |
[
{
"content": "Determine the set of real numbers $a$ for which the series \\( \\sum_{n=1}^\\infty \\sin\\left(\\pi \\sqrt{n^2+a^2} \\right) \\) converges.",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $2,723.11 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.0361 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 67.9 g |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1250 W |
[
{
"content": "Evaluate the Lebesgue integral: $$\\int_{\\mathbb{R}} 1 \\, d\\lambda(t).$$",
"role": "user"
}
] | \infty |
[
{
"content": "Evaluate the integral \\( \\int_{\\gamma} d\\omega \\), where \\( \\omega = (y+z)\\,dx + (z+x)\\,dy + (x-y)\\,dz \\) and \\( \\gamma \\) is the intersection of the spherical surface \\( x^2 + y^2 + z^2 = 1 \\) with the plane \\( y = z \\). Use the parametrization \\( x = \\cos t, \\ y = \\frac{1}{... | 0 |
[
{
"content": "Let $K$ be a field, $A$ be a finite-dimensional $K$-algebra, and $M$ be a finitely generated $A$-module. Determine whether $M$ admits a projective resolution by finitely generated projective $A$-modules.",
"role": "user"
}
] | Yes |
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