f1[[CurlyPhi]Rational, sRational, [Theta]Rational, aRational] = ( Sqrt[s](a - s))/((a - s)^2 + a^2 - 2a(a - s)Cos[[CurlyPhi] - [Theta]])

NIntegrate[
 f1[\[CurlyPhi], s, 4*Pi/20, 1], {\[CurlyPhi], 0, Pi}, {s, 0, 1}]

When Phi equals 0, it cannot be calculated.
Note: the Rate of convergence of Numerical integration is too slow and the integration value is overflow、Indeterminate or Infinity

When Phi equals 4*Pi/20, the result is 4.10626.
Note: the Rate of convergence of Numerical integration is too slow and cannot converge to the specified accuracy

Is there anyone who can help solve this problem? Thank you very much