\( \int \int _ { s } f ( x , y , z ) d s = \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 2 \pi } f ( s ( \phi , \theta ) ) \| \frac { \partial s } { \partial \phi } \times \frac { \partial s } { \partial \theta } \| d \theta d \phi \)

The equation shows that the surface integral of a function \( f(x, y, z) \) over a surface \( s \) can be calculated by parameterizing the surface with angles \( \phi \) and \( \theta \), and integrating the function multiplied by the area element \( \| \frac{\partial s}{\partial \phi} \times \frac{\partial s}{\partial \theta} \| \) over the parameter ranges \( \phi \) from \( 0 \) to \( \pi \) and \( \theta \) from \( 0 \) to \( 2\pi \).