Question: Things getting too complicated

Hi

I have this

diff(q^2*l(a, q)^(1/2)*((1-l(a, q))/(1.1))^(1/2)+(1-a)*(1-q*l(a, q)^(1/2))*q*((1-l(a, q))/(1.1))^(1/2)+a*(1-q*((1-l(a, q))/(1.1))^(1/2))*q*l(a, q)^(1/2), a)

where l(a,q) signifies that l is function of a and q, specifically

RootOf((330578512439669421489*sqrt(1-a)*q^2*sqrt(a)-330578512439669421489*sqrt(1-a)*q^2-330578512439669421489*sqrt(a)*q^2+330578512439669421489*q^2)*_Z^4+(-165289256228925619836*q-165289256228925619836*sqrt(1-a)*sqrt(a)*q+165289256228925619836*q*a+165289256228925619836*sqrt(1-a)*q)*_Z^3+(41322314059504132232-330578512421487603306*sqrt(1-a)*q^2*sqrt(a)-330578512421487603306*q^2+4132231395495867768*a+330578512421487603306*sqrt(1-a)*q^2+330578512421487603306*sqrt(a)*q^2)*_Z^2+(82644628109917355372*sqrt(1-a)*sqrt(a)*q-82644628109917355372*q*a+82644628109917355372*q-82644628109917355372*sqrt(1-a)*q)*_Z-45454545455000000000*a+82644628100826446281*q^2-82644628100826446281*sqrt(1-a)*q^2+82644628100826446281*sqrt(1-a)*q^2*sqrt(a)-82644628100826446281*sqrt(a)*q^2)^2

I want the the integral from 0 to 1 over q of the top equation to be set to zero and then solve for a (the first order condition to pin down a), but thing get too big and maple gives up

is there a better way to do this?

Thanks