Find the volume of the region bounded by $z=x^3 + y^2 $, $z=0$, $-a<x<a$, and $-a<y<a$

Question

Since $z \geq 0$ then,

$x^3+y^2 \geq 0 \rightarrow x \geq -y^{2/3}$

So, I set up the integral as follows:

$$V = \int_{-a}^{a} \int_{-y^{2/3}}^{a} (x^3+y^2) \, dx \, dy$$

However, according to wolfram alpha the above integral evaluates to $0$. The correct answer according to the textbook should be $\frac{8a^4}{3}$. Not sure where I messed up. Any insight would be highly appreciated!