I have a function, S[q] which is obtained by integrating another function, A[r,q] over r.

My problem is that the lower limit of integration,
rmin depends on q in a complicated manner. Mathematica can however solve this equation to give several routes, only one of which is real which is the one I want.

I have a second function too, L[q] which is also obtained by integrating B[r,q] over r. Again the lower limit of integration depends on q in the same manner.

What I want to do is for a given value of q, solve
the equation for rmin, and use this to calculate
the corresponding L[q]. I then wish to calculate
S[q] in the same manner.

I want Mathematica to do this for many values of
q over a range and use the results to plot
S[q] against L[q]. Does anyone know an efficient
way to do this?

Thank you for your help.