How to Solve an Equation with Integral and Gamma functions?

Hello

Dear all,

I need to solve an equation, L, that includes a second function, F, that also includes the lower incomplete gamma function, gammainc. Unfortunately, I cannot correctly program it in MATLAB.I appreciate your help. Please see the pictures attached to see the functions (L and F).

P.S. I initially attempted to solve it through numerical integration (trapz), but my results are not correct! The correct results should look like the second attached picture.

Note that the parameter s is an array (e.g. s = 0.015), or a vector (s = 0.015:0.001:0.1)

I really appreciate your response in advance.