Let F(x, y, z) = (xz — eª, 2xy + sin y, −yz + tan¯¹ z). Let S be the surface defined by R(u, v) = (u², uv, v²) with 0 ≤ v ≤ u and 0 ≤ u ≤ √√5. Find the flux of curl F across the positively-oriented surface S.

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