7. For a planar region $D$, let $N(D)$ denote the number of all lattice points belonging to $D$. If $A$ represents the region (including boundaries) enclosed by the curve $y=x^{2}(x \leqslant 0)$ and the two lines $x=-10, y=1$, and $B$ represents the region (including boundaries) enclosed by the curve $y=x^{2}(x \geqslant 0)$ and the two lines $x=1, y=100$, what is the value of $N(A \cup B)+N(A \cap B)$?
7. Regions $A$ and $B$ are as shown in Figure 31-7. By the symmetry of the parabola $y=x^{2}$, the symmetric region of $A$ with respect to the $y$-axis is $C$. Therefore, the number of lattice points inside and on the boundary of region $A$ is the same as that of region $C$, so $N(A)+N(B)=N$ (rectangle $E F G H)+N$ (parabola arc $E G)=1010$ (points).
$$
\text { Also, } A \cap B=\varnothing \text {, so } N(A \cup B)+N(A \cap B)=1010 \text { (points). }
$$