Unfortunately I still have this problem.

I can do like this:

E_theta := evalf(sum('((W*V0[i]*sqrt(epsre))/(2*Pi*Z0))^2*((cos(Pi*sin(theta)/(2*sqrt(epsre))))^2)/(epsre - (sin(theta))^2)^2*((epsr - (sin(theta))^2)*(cos(theta))^2)/((epsr - (sin(theta))^2) + epsr^2*(cos(theta))^2*(cot(k0*h*sqrt(epsr - (sin(theta))^2)))^2)', 'i' = 1..80)):

E_phi := evalf(sum('((W*V0[i])/(2*Pi*Z0))^2*(cos(theta))^2/((epsr - (sin(theta))^2)*cot(k0*h*sqrt(epsr - (sin(theta))^2))^2 + (cos(theta))^2)*(piecewise(l*k0*sin(theta)/2=0, 1, sin(l*k0*sin(theta)/2)/(l*k0*sin(theta)/2)))^2', 'i' = 1..80)):

In this case I have got the answer. But I am not sure that this is correct...

Thank you. I noticed this mistake. I replaced operator ":=" by "=".

"What do you mean by "I am looking for E_phi(theta), E_theta(theta), E_horiz(phi)."?" I mean that I would like to find three complex expressions E_phi, E_theta, E_horiz which are determined by two variables theta and phi.

I have done one more mistake. Here "Maple cannot solve this line: "E_phi_magnitude := sqrt((Re(E_phi))^2 + (Im(E_phi))^2):"." I would like to say that Maple cannot find this "E_horiz := sqrt(E_theta^2 + E_phi^2):". There is no equation. E_horiz is the complex expression.

"Since there are lots of names involved having no numeric values there is not much simplification that can be done." This is just a part of my program. All of the variables (except theta and phi) are determined above. I can show the whole prgram if it is possible.

This is a part of my calculations.

V0 := array(1..80):
for i from 1 to 80 do
V0[i] := JX[i]*Z0*((Pi/l)^2 - kx^2)/((2*Pi/l)*cos(kx*l/2)*(piecewise(ky*l/2=0, 1, sin(ky*l/2)/(ky*l/2))))
end do:
E_theta := sum('((W*V0[i]*sqrt(epsre))/(2*Pi*Z0))^2*((cos(Pi*sin(theta)/(2*sqrt(epsre))))^2)/(epsre - (sin(theta))^2)^2*((epsr - (sin(theta))^2)*(cos(theta))^2)/((epsr - (sin(theta))^2) + epsr^2*(cos(theta))^2*(cot(k0*h*sqrt(epsr - (sin(theta))^2)))^2)', 'i' = 1..80):
E_theta := subs(phi = 0, theta = Pi/2 - theta, E_theta):
E_theta_magnitude := sqrt((Re(E_theta))^2 + (Im(E_theta))^2):
E_phi := sum('((W*V0[i])/(2*Pi*Z0))^2*(cos(theta))^2/((epsr - (sin(theta))^2)*cot(k0*h*sqrt(epsr - (sin(theta))^2))^2 + (cos(theta))^2)*(piecewise(l*k0*sin(theta)/2=0, 1, sin(l*k0*sin(theta)/2)/(l*k0*sin(theta)/2)))^2', 'i' = 1..80):
E_phi := subs(phi = Pi/2, theta = Pi/2 - theta, E_phi):
E_phi_magnitude := sqrt((Re(E_phi))^2 + (Im(E_phi))^2):
E_horiz := sqrt(E_theta^2 + E_phi^2):
E_horiz := subs(theta := Pi/2, E_horiz):
E_horiz_magnitude := sqrt((Re(E_horiz))^2 + (Im(E_horiz))^2):

I am looking for E_phi(theta), E_theta(theta), E_horiz(phi).
Maple cannot solve this line: "E_phi_magnitude := sqrt((Re(E_phi))^2 + (Im(E_phi))^2):".
Could you help me to find my mistake?

I know that I have to get two answers in this case, but I cannot solve this equation. Maple cannot find the solution.
If my explanation is not clear I can give an example.