Customizable Integral of Square Root

Students of math often get confused about what it means to rotate the integral function around the x-axis. This Customizer allows for the generation of 3d models depicting the integral of a square root in various configurations. As this is a work-in-progress, there may still be unknown bugs. Please comment if you encounter any of these bugs.
Note that the Customizer preview is inaccurate, and the final model looks very different than the image in the preview.

I also made a short video in POV-Ray using models from this: https://youtu.be/YdLTYTfzx34

For those interested, the files for POV-Ray are included here.