I need to confirm my own numerical calculation of the following integral with another package - possibly one that calculates to more decimal places. If someone can point me to such software or confirm the result I'd be grateful.

Integral=2553.871 when r=5 & R=27 (angles in radians)

I've derived some possible equations for the integral but they are all giving results that are less than 1% from the numerical results, so I can't tell if the equations are wrong or the numerical answers are wrong.

For example, one equation generates an answer of 2551.2952, another 2553.5994.

If someone could plug in other values of r & R and supply the results, that would also be great.