Let $I$ be the flux of $\mathbf{G} = \left<3 e^y,6x^{5}e^{x^{6}},0\right>$ through the upper hemisphere $\mathcal{S}$ of the unit sphere.

(a) Find a vector field $\mathbf{A}$ such that $\text{curl}(\mathbf{A})=\mathbf{G}$.
(b) Calculate the circulation of $\mathbf{A}$ around $\partial \mathcal{S}$.
(c) Compute $I$, the flux of $\mathbf{G}$ through $\mathcal{S}$.

(a) $\mathbf{A}=$
(b) $\int_{\mathcal{C}} \mathbf{A}\cdot d\mathbf{s}=$
(c) $I =$