inclusionAI/Ring-lite-rl-data huggingface dataset:
A square table consists of a tabletop and four legs. If 1 cubic meter of wood can be used to make 50 tabletops or 300 legs, and there are 5 cubic meters of wood available, please design how many cubic meters of wood should be used to make tabletops so that the number of tabletops matches the number of legs exactly, with neither leftover.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
$P\left(x\right)$ is a polynomial of degree at most $6$ such that such that $P\left(1\right)$, $P\left(2\right)$, $P\left(3\right)$, $P\left(4\right)$, $P\left(5\right)$, $P\left(6\right)$, and $P\left(7\right)$ are $1$, $2$, $3$, $4$, $5$, $6$, and $7$ in some order. What is the maximum possible value of $P\left(8\right)$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{
312
}
Find the kernel of the homomorphism \( D: F[x] \to F[x] \) defined by \( D(f(x)) = f'(x) \), where \( f(x) = a_0 + a_1x + \cdots + a_nx^n \) and \( f'(x) = a_1 + 2a_2x + \cdots + na_nx^{n-1} \), given that the characteristic of the field \( F \) is \( p \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{F[x^p]}
There are 5 teachers available to lead 3 extracurricular groups for an educational field trip. Each group can have at most 2 leaders, but neither teacher A nor teacher B can lead a group on their own. How many different leadership arrangements are possible? (Answer in numerals).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{54}
Let $A_1A_2A_3A_4$ be a square, and let $A_5, A_6, A_7, \ldots, A_{34}$ be distinct points inside the square. Non-intersecting segments $\overline{A_iA_j}$ are drawn for various pairs $(i,j)$ with $1 \le i,j \le 34$, such that the square is dissected into triangles. Assume each $A_i$ is an endpoint of at least one of the drawn segments. How many triangles are formed?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{62}
For each positive integer $n$, let $a(n)$ be the number of zeros in the base 3 representation of $n$. For which positive real numbers $x$ does the series $$ \sum_{n=1}^{\infty} \frac{x^{a(n)}}{n^3} $$ converge? Please provide the sum of the endpoints of the interval for which the series converges.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25}
Two trains of different lengths are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. The longer train is 280 m long. They will be clear of each other in 16.998640108791296 seconds from the moment they meet. What is the length of the shorter train?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{59.97}
A square is made by arranging 12 marbles of the same size without gaps in both the width and length. How many marbles are placed around the perimeter?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{44}
设函数 f:\{1,2,3\}\rightarrow\{2,3,4\} 满足 f[f(x)-1]=f(x)，则这样的函数有__________个.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
21 Savage has a 12-car garage, with a row of spaces numbered 1, 2, 3, \ldots, 12. How many ways can he choose 6 of them to park his 6 identical cars in, if no 3 spaces with consecutive numbers may be all occupied?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{357}
To get to school, Jenny decided to ride the school's double decker bus. The bus has a total of 25 rows of seats, with 15 rows on the lower deck and 10 rows on the upper deck. On the lower deck, each row has a capacity of 5 kids, while on the upper deck, each row can seat up to 3 kids. Additionally, 4 staff members must also ride the bus. Any vacant seat can be occupied by any person who possesses a ticket, either lower or upper deck ticket, except for the reserved seats.

On the lower deck, 10 students were given reserved seats, which only they can sit in. There are 4 types of bus tickets: Premium lower deck, Regular lower deck, Premium upper deck, and Regular upper deck. Premium ticket holders have priority to sit on the first row of each deck.

Considering staff members count towards the number of ticketed occupants, reserved seats for specific students, and the priority seating policy, find the maximum number of different kids that can ride the school bus.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{91}
In the plane Cartesian coordinate system \(xOy\), point \(P\) is a moving point on the line \(y = -x - 2\). Two tangents to the parabola \(y = \frac{x^2}{2}\) are drawn through point \(P\), and the points of tangency are \(A\) and \(B\). Find the minimum area of the triangle \(PAB\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3\sqrt{3}}
Let the real numbers \( a \) and \( b \) satisfy \( a = x_1 + x_2 + x_3 = x_1 x_2 x_3 \) and \( ab = x_1 x_2 + x_2 x_3 + x_3 x_1 \), where \( x_1, x_2, x_3 > 0 \). Then the maximum value of \( P = \frac{a^2 + 6b + 1}{a^2 + a} \) is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{9 + \sqrt{3}}{9}}
Let the equation 
\[ 
1 + x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \cdots - \frac{x^{2018}}{2018} = 0 
\]
have all its real roots within the interval \([a, b]\), where \(a\) and \(b\) are integers such that \(a  b\). What is the minimum value of \(b - a\)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Task 1. We call a collection of lines in the plane beautiful if each line in the collection intersects an odd number of the other lines in the collection.

Determine the smallest integer $k \geq 0$ with the following property: for any 2018 different lines $\ell_{1}, \ell_{2}, \ldots, \ell_{2018}$ in the plane, there exist lines $\ell_{2018+1}, \ell_{2018+2}, \ldots$, $\ell_{2018+k}$ such that the lines $\ell_{1}, \ell_{2}, \ldots, \ell_{2018+k}$ are all different and form a beautiful collection.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1010}
Two groups, Group A and Group B, each have 10 students who took a math test. The scores are as follows (unit: points):
Group A: $76$, $90$, $84$, $86$, $81$, $87$, $86$, $82$, $85$, $83$
Group B: $82$, $84$, $85$, $89$, $79$, $80$, $91$, $89$, $79$, $74$
Now, one student is randomly selected from these 20 students. Let event $A$ be "the selected student is from Group A" and event $B$ be "the selected student scored at least $85$ points on the math test." Calculate $P(A|B)$, the probability that the selected student is from Group A given that the student scored at least 85 points. Express your answer as a simplified fraction.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{5}{9}}
Find all values of the variable \( x \) for which both expressions \( f(x)=\sqrt{21-x^{2}-4x} \) and \( g(x)=|x+2| \) are defined, and such that \( \min (f(x), g(x)) > \frac{x+4}{2} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{x \in \left[-7, -\frac{8}{3}\right) \cup (0, 2)}
$A$ and $B$ play the following game: random \( k \) numbers are chosen from the first 100 positive integers. If the sum of these is even, $A$ wins; otherwise, $B$ wins. For which values of \( k \) are the winning chances of \( A \) and \( B \) equal?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{k \text{ is odd }}
A function f(x) is defined on the set of real numbers and is odd. It satisfies f(3) = 0, and when x > 0, the inequality f(x) > -xf'(x) holds. Determine the number of zeros of the function g(x) = xf(x) + log|x+1|. Express your answer as a whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Sarah, an Australian political science student, loves analyzing historical election results. She decides to look at the election outcomes in her country for the past 60 years. She finds that there were 15 federal elections during this period. Each election had an average of 6 major parties competing.

Sarah is particularly interested in the number of seats won by each party and discovers the following pattern: In each election, the party that won the most seats typically secured 35% of the total available seats. She learns that on average, each election had 150 seats available.

If Sarah wants to calculate the total number of seats won by the leading parties across all 15 federal elections, how many seats did they win in total?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{788}
Find the measure of angle \( B \widehat{A} D \), given that \( D \widehat{A C}=39^{\circ} \), \( A B = A C \), and \( A D = B D \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{47^\circ}
Let $\{a_n\}$ be a sequence of integers satisfying the recurrence relation:
\[
(n-1)a_{n+1} = (n+1)a_n - 2(n-1) \quad \forall n \ge 1.
\]
Given that $2000 \mid a_{1999}$, determine the smallest integer $n \ge 2$ such that $2000 \mid a_n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{249}
Triangle  $ABC$  lies entirely in the first quadrant of the Cartesian plane, and its sides have slopes  $63$ ,  $73$ ,  $97$ . Suppose the curve  $\mathcal V$  with equation  $y=(x+3)(x^2+3)$  passes through the vertices of  $ABC$ . Find the sum of the slopes of the three tangents to  $\mathcal V$  at each of  $A$ ,  $B$ ,  $C$ .

*Proposed by Akshaj*
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{237}
9. In a rectangular box $A B C D E F G H$ with edge lengths $A B=A D=6$ and $A E=49$, a plane slices through point $A$ and intersects edges $B F, F G, G H, H D$ at points $P, Q, R, S$ respectively. Given that $A P=A S$ and $P Q=Q R=R S$, find the area of pentagon $A P Q R S$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{141\sqrt{11}}{2}}
Let $d_1$, $d_2$, $d_3$, $d_4$, $e_1$, $e_2$, $e_3$, and $e_4$ be real numbers such that for every real number $x$, we have
\[
  x^8 - 2x^7 + 2x^6 - 2x^5 + 2x^4 - 2x^3 + 2x^2 - 2x + 1 = (x^2 + d_1 x + e_1)(x^2 + d_2 x + e_2)(x^2 + d_3 x + e_3)(x^2 + d_4 x + e_4). 
\]
Compute $d_1 e_1 + d_2 e_2 + d_3 e_3 + d_4 e_4$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2}
In triangle \( \mathrm{ABC} \), side \( AB = 4 \) and side \( BC = 6 \). Point \( M \) lies on the perpendicular bisector of segment \( AB \), and lines \( AM \) and \( AC \) are perpendicular. Find \( MA \), given that the circumradius of triangle \( ABC \) is 9.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
A company has 100 shareholders, and any 66 of them together own at least 50% of the company's shares. What is the maximum percentage of all shares that one shareholder can own?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{25 \%}
4. Let set $A=\{1,2,3, \cdots, 1997\}$, for any 999-element subset $X$ of $A$, if there exist $x, y \in X$, such that $x<y$ and $x \mid y$, then $X$ is called a good set. Find the largest natural number $a(a \in A)$, such that any 999-element subset containing $a$ is a good set.
(《Mathematics in Middle School》1999 Issue 1 Olympiad Problems)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{665}
Emily is thinking of a number. She gives the following 3 clues. "My number has 216 as a factor. My number is a multiple of 45. My number is between 1000 and 3000." What is Emily's number?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2160}
What is the correlation coefficient between $X_{(1)}$ and $X_{(3)}$ when they are order statistics of three independent random variables $X_1, X_2, X_3$, each uniformly distributed in the interval $[0,1]$? It is given that $X_{(k)}$ follows a Beta distribution with parameters $k$ and $4-k$. Utilize the theorem for covariance to compute the correlation coefficient, where the variance of $X_{(k)}$ is $\frac{k(4-k)}{80}$ and its mean is $\frac{k}{3}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/3}
Two motorcyclists departed simultaneously from points \( A \) and \( B \) towards each other and met 50 km from point \( B \). After arriving at points \( A \) and \( B \), the motorcyclists immediately turned back and met for the second time 25 km from point \( A \). How many kilometers are there from \( A \) to \( B \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{125}
Evaluate the following limit using Taylor expansion:

$$\lim_{x\to0^+} \frac{\log(\vert x \vert (1+x^2)^{1/3}-\sin{x})}{\log(\vert x \vert)}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
If the range q of the 6 numbers 4, 314, 710, and x is 12, what is the difference between the greatest possible value of x and the least possible value of x?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{682}
The pentagon \(A B C D E\) is circumscribed about a circle.

The angles \(\angle A B C\), \(\angle B A E\), and \(\angle C D E\) are each \(104^{\circ}\). Find \(\angle A D B\). Provide the answer in degrees (only the number, without specifying the unit of measurement).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{38}
In $\triangle ABC$, it is known that $\angle B=45^\circ$, $AC=\sqrt{2}BC$. Find $\angle C=$______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{105^\circ}
Calculate the integral \( \int_{C} f(z) \, dz \), where \( f(z) = \frac{\bar{z}}{z+i} \) and \( C \) is the circle \( |z+i|=3 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-2\pi}
In $R^5$ with coordinates $(p_1,q_1,p_2,q_2,t)$, $db=dp_1\wedge dp_2$. Calculate the integral $\int_T db\wedge dt$, where $T=\{t\in[0,1],p_1^2+q_1^2=p_2^2+q_2^2\leq t^2\}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
We place four spheres of radius $r$ on a horizontal plane so that their centers form a square and they touch each other. We then place a fifth sphere of radius $r$ on top of the four spheres, touching all four of them. How far is the highest point of the fifth sphere from the plane? (H)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{r\sqrt{2}+2r}
Figure F represents the intersection of \( n \) circles ( \( n \geq 2 \), radii are not necessarily equal). What is the maximum number of curved "sides" that Figure F can have? (A curved side is a segment of the boundary of F that belongs to one of the circles and is bounded by intersection points with other circles.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2n-2}
A courtyard is 28 meters long and 13 meters wide and is to be paved with bricks of dimensions 22 cm by 12 cm. How many bricks are required to pave the entire courtyard?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13,788}
The side length of a rhombus is $a$ and its acute angle is $\alpha$. The rhombus rotates around a line passing through its vertex and parallel to the larger diagonal. Find the volume of the solid of revolution.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 \pi a^3 \sin \frac{\alpha}{2} \sin \alpha}
In tetrahedron \(ABCD\), \(AB = 1\), \(BC = 5\), \(CD = 7\), \(DA = 5\), \(AC = 5\), \(BD = 2\sqrt{6}\). Find the distance between skew lines \(AC\) and \(BD\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3\sqrt{11}}{10}}
A tank holds x gallons of a saltwater solution that is 25% salt by volume. One third of the water is evaporated, leaving all of the salt. Then, 12 gallons of water and 24 gallons of salt are added, raising the salt percentage to 40%. After this, another one fourth of the water is evaporated, leaving the salt once again. In the final step, 15 gallons of water and 30 gallons of salt are added, resulting in a mixture that is 50% salt by volume. What is the value of x?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{192}
There are fifteen boxes, each containing either a white ball or a black ball, with no more than 12 white balls in total. You can choose any three boxes and ask, "Does any of these three boxes contain a white ball?" and receive a truthful answer. What is the minimum number of questions you need to ask to ensure you find at least one white ball?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Given vectors $\overrightarrow {a}$=(2,$m$), $\overrightarrow {b}$=(-1,2), if $\overrightarrow {a}$⊥$\overrightarrow {b}$, then the projection of $\overrightarrow {b}$ on vector $\overrightarrow {c}$=$\overrightarrow {a}$-$ \overrightarrow {b}$ is ___.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{- \frac { \sqrt {10}}{2}}
One autumn day, a Scattered Scientist glanced at his antique wall clock and saw three flies asleep on the dial. The first one was exactly at the 12 o'clock mark, and the other two were precisely at the 2 o'clock and 5 o'clock marks. The Scientist measured and determined that the hour hand posed no threat to the flies, but the minute hand would sweep them all away one by one. Find the probability that exactly two of the three flies will be swept away by the minute hand precisely 40 minutes after the Scientist noticed the flies.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{2}}
What is the area of the largest rectangle that can be inscribed within an ellipse given by the equation $\frac{(x-y)^2}{2m^2} + \frac{(x+y)^2}{2n^2} = 1$, where $0<mn\leq 1$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2mn}
For positive integers $n,$ let $\tau (n)$ denote the number of positive integer divisors of $n,$ including 1 and $n.$ Define $S(n)$ by $S(n)=\tau(1)+ \tau(2) + \cdots + \tau(n).$ Let $a$ denote the number of positive integers $n \leq 3000$ with $S(n)$ odd, and let $b$ denote the number of positive integers $n \leq 3000$ with $S(n)$ even. Find $|a-b|.$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{54}
Given real numbers $x$ and $y$ satisfying $2x^2 + xy - y^2 = 1$, find the maximum value of $\frac{x - 2y}{5x^2 - 2xy + 2y^2}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\sqrt{2}}{4}}
Compute the following expression:  
\[ \sum_{i=0}^{\frac{q-1}{2}}\left\lfloor\frac{ip}{q}\right\rfloor + \sum_{j=0}^{\frac{p-1}{2}}\left\lfloor\frac{jq}{p}\right\rfloor \]  
where \( p = 51 \) and \( q = 81 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1001}
A trader sells three different articles, A, B, and C, each with varying profit percentages (10%, 20%, and 30%, respectively) and individual selling prices of $100, $150, and $200, respectively. If he then sells each article for twice its initial selling price, determine his overall profit percentage for selling all three articles.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{143.4\%}
12.222. The base of the pyramid is a rhombus, one of the angles of which is $\alpha$. The lateral faces are equally inclined to the plane of the base. A plane is drawn through the midpoints of two adjacent sides of the base and the vertex of the pyramid, forming an angle $\beta$ with the plane of the base. The area of the resulting section is $S$. Find the side of the rhombus.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\sqrt{\frac{2S\cos\beta}{\sin\alpha}}}
Ronald wants to make profits by re-selling some phones he bought a week ago. He bought 200 units for just $3000, and he wants to gain a third of the initial investment in profits when all units are sold. Additionally, there is an 8% sales tax on each sale, and he must also account for $2 per unit for packaging and a $500 flat shipping fee for the entire lot. Taking all these costs into consideration, what will be the selling price for each phone, including tax?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$26.46}
The function \( f(x) = \max \left\{\sin x, \cos x, \frac{\sin x + \cos x}{\sqrt{2}}\right\} \) (for \( x \in \mathbb{R} \)) has a maximum value and a minimum value. Find the sum of these maximum and minimum values.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1 - \frac{\sqrt{2}}{2}}
Find $w$, such that $5^65^w=25$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-4}
Let  $a_1$ ,  $a_2, \dots, a_{2015}$  be a sequence of positive integers in  $[1,100]$ .
Call a nonempty contiguous subsequence of this sequence *good* if the product of the integers in it leaves a remainder of  $1$  when divided by  $101$ .
In other words, it is a pair of integers  $(x, y)$  such that  $1 \le x \le y \le 2015$  and \[a_xa_{x+1}\dots a_{y-1}a_y \equiv 1 \pmod{101}. \]Find the minimum possible number of good subsequences across all possible  $(a_i)$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19320}
已知函数$f\left( x \right)={{\left( \frac{1}{5} \right)}^{x}}-\text{1},x\in \left[ -1,0 \right]$，$g\left( x \right)={{a2}}\text{lo}{{\text{g}}_{2}}x\text{+3}a,x\in \left[ \frac{\sqrt{2}}{2},2 \right]$，若对任意的${{x0}}\in \left[ \frac{\sqrt{2}}{2},2 \right]$，总存在${{x}_{1}}\in \left[ -1,0 \right]$使得$g\left( {{x0}} \right)=f\left( {{x}_{1}} \right)$成立，则实数$\textit{a}$的取值范围是__________．
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$0\le a\le 1$}
There are $2022$ distinct integer points on the plane. Let $I$ be the number of pairs among these points with exactly $1$ unit apart. Find the maximum possible value of $I$. 
([i]Note. An integer point is a point with integer coordinates.[/i])

[i]Proposed by CSJL.[/i]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3954}
Arrange 6 volunteers $A$, $B$, $C$, $D$, $E$, $F$ to take care of 3 elderly people $X$, $Y$, $Z$. Each pair of volunteers takes care of one elderly person. Considering the distance between the volunteers' and the elderly people's residences, volunteer $A$ cannot be assigned to take care of elderly person $X$, and volunteer $B$ cannot be assigned to take care of elderly person $Y$. Calculate the total number of different arrangements.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{42}
We are downloading a 1.5 MB file to our computer from the internet. During this process, the program continuously estimates the remaining time based on the average speed of the download so far. At one moment, we observe that exactly half of the file has already been downloaded, and at this moment, the program estimates that the remaining time is precisely 2 minutes. After this time, regardless of any $t$ time that passes (due to network congestion), the program still indicates that the remaining time to download the file is 2 minutes. Determine the size of the file that has already been downloaded as a function of $t$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3 + 1.5t}{4 + t} \text{ MB}}
Determine the radius of the smallest disc in the complex plane that contains all eigenvalues of the matrix A, given that the characteristic polynomial of A - I is x^4 + 15x^2 - 14x + 16, where I is the identity matrix.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Let $N = 99999$. Then $N^3 = \underline{\quad\quad}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{999970000299999}