$S$ is parametrized by $X(s,t) = (s\cos(t), s\sin(t), t)$, $0 \leq s \leq 1$ and $0 \leq t \leq \frac{\pi}{2}$
$\mathbf{F} = z \mathbf{i} + x \mathbf{j} + z \mathbf{k}$
I have two things preventing me from solving this: first, I do not know how to find $d\,\mathbf{s}$ for $X(s,t) = (s\cos(t), s\sin(t), t)$ and I am not sure how to take out the parameterization of $X$ and find a surface to work with for the double integral over $s$ of $\nabla x \mathbf{F} \,d\,\mathbf{S}$