Calculate the integral of $f(x,y,z) = 3 x^2+3 y^2+z^{6}$ over the curve $\mathbf{c}(t) = (\cos t, \sin t, t)$ for $0\le t\le \pi$.

$\int_{\mathcal{C}} (3 x^2+3 y^2+z^{6}) \,ds =$