Calculate the total flux of vector filed $F$ through plane $D$ if $F$ is given by $F (x, y, z) = (-y, x, x ^ 2)$,

Question

Calculate the total flux of vector filed $F$ through plane $D$ if $F$ is given by $F (x, y, z) = (-y, x, x ^ 2)$, and $D$ is a union of cylinder $x ^ 2 + y ^ 2 = a ^ 2$ where we take $ z \in [0, h] $ and with upper roller base.
My solution:
I have to calculate integral of upper roller base $F$ dot product with unit normal (in this case in would be $<0,0,1>$) so I would left with only z part of my vector filed $x^2$ and if I integrate that on circle radius $a$ I get $\pi \frac{a^4}{4}$.
I have to calculate integral of roller base $F$ dot product with unit normal (in this case in would be $<x,y,0>*\frac{1}{a}$), but $<-y,x,x^2>*<x,y,0>\frac{1}{a}=0$ So the flux must be $\pi \frac{a^4}{4}$, but the textbook give another solution, so what I did wrong.