Volume of a bead with square hole- Program approach?

[DM48]

\(\frac{4}{3}+\left ( -2b^2\sqrt{a^2-2b^2}\;a^3\pi+2a^3\;arccot \left( \frac{a\sqrt{a^2-2b^2}}{b^2} \right)+2b\left(-3a^2+b^2 \right )arctan\left(\frac{b}{\sqrt{a^2-2b^2}} \right ) \right )\)

Another solution by someone else. This assumes (I think) a = radius of sphere and b = square dimension (no rectangle solution).