Help for a "Surface and Flux integrals" program

[salvomic]

I can't solve this problem; I'm following a book that perhaps report a wrong result: (π/6)*(5^(3/2)-1) -> 5.33041350027

Area of a paraboloid with cartesian equation z=x^2+y^2, integrated in a circumference with center in 0,0 and radius 1; we have x=u, y=v, z=u^2+v^2
We want calculate the area of the surface, so the function treated is constant 1.
The book suggest
\[ \int_{\sigma }1dS=\iint\sqrt{4u^2+4v^2+1}dudv=\int_{0}^{1}\int_{0}^{2\pi }\rho \sqrt{1+4\rho ^2}d \rho d\theta = \frac{\pi }{6} (5^\frac{3}{2}-1) \]
passing to the polar coordinates...
The Prime return another number for the integral (see attached image) and not \( \frac{\pi }{6} (5^\frac{3}{2}-1) \) that's about 5.33041350027.
Prime return 166.85...
So my previous example was so strange to test sfint()...
sfint(1,[u,v,u^2+v^2],[0,1],[0,1]) returns another number: 1.861564...

Salvo