Question: Compute (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given oriented surface or parametrized surface. (mathbf{F}(x, y, z)=leftlangle 0,0, x z e^{x y}ightangle, quad z=x y,

Compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface or parametrized surface.
$\mathbf{F}(x, y, z)=\left\langle 0,0, x z e^{x y}ightangle, \quad z=x y, \quad 0 \leq x \leq 1,0 \leq y \leq 1$, upward-pointing normal

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