Can I ask question which require very high accuracy calculation with very delicate nature on MO :

Ex: calculate: $$S(q)=\int_{x=2}^q\sin^2\left(\frac{π\Gamma(x)}{2x}\right)dx$$ for $q=10^3$ or $10^4$

Mathematica doesn't seem to help me with this.

This will require very high efficiency calculation

Is there any other forum where I can put this type of question ?