How to use The  value of lambda in other operation ?

solve({alpha = (1/2)*lambda*alpha*Pi, beta = (1/2)*lambda*beta*Pi}, lambda)

for exampel 

lambda^6;

example of non linear fractional integraL Equation 

x(t)=(t^3)+1/5 * x(t) * I^(1/2)x^2

how input the integral fraction int(^1/2) for the any function in maple ? 

How to compute integral of complicated function in maple 

int(e^(-s)*ln(1+s*e^-s)ds)from 0 to t 

i can not computed and how to simplify the integral because the wieght of calculation is to big?