Some hints:
- Omit the darn clear all, which causes more troubles than it solves.
- Provide the function to be integrated as function handle, not as string. The string method is still working to keep the backward compatibility, but it is outdated for 20 years now.
- 1./x is much more efficient that x.^-1
We cannot guess, which "angle" you set where from 45 to 50. Without any useful comments the code is a graveyard for numbers and trigonometric functions only. Use trailing semicolons to suppress the time-consuming output to the command window.
The error message occurs, if there is a pole at the initial position.
