It's hard to say if something like this will work universally since I don't know the nature of your functions, but you can do something like this with the symbolic math toolbox:
syms a1 a2 a3 y
f = a1+a2.*y+a3.*y.^2;
g = a1.*y+a2+a3.*y.^2;
h = a1.*y.^2+a2.*y+a3;
H = 5;
m = int(f,y,0,H)
n = int(g,y,0,H)
p = int(int(h,y,0,y),y,0,H)
answer = solve(m==1,n==2,p==3)
I set m, n and p equal to the equations themselves, then in the solve argument I solve for them to be equal to some known values. In this case, it would translate such that your m = 1, n = 2 and p = 3. The functions f, g and h are defined arbitrarily.
I think you could also accomplish this with the '\' operator in base MATLAB if you knew values of y as well.
