Triple integrals in Spherical coordinates

This applet helps to visualize simple solids \(E\) in spherical coordinates of the following form:

• \( \alpha \leq \phi \leq \beta \)
• \( \theta_1(\phi) \leq \theta \leq \theta_2(\phi) \)
• \( \rho_1(\phi,\theta) \leq \rho \leq \rho_2(\phi,\theta) \)

So \( \phi \) is independent, \( \theta \) possibly depends on \( \phi \) and \( \rho \) possibly depends on both \(\phi,\theta \). Enter the corresponding bounds in the boxes, enter \( \phi \) as \( 'p' \) and \(\theta \) as \( 't' \).