= Solution
Set $G=\rho g(\sin\alpha-\cos\alpha H_x)$. For downstream shear $G\geq0$, <Glen's flow law> and the <no-slip boundary condition> give
$$
u(x,z)=A G^n\int_0^z(H-z')^n\,dz'=\frac{AG^n}{n+1}[H^{n+1}-(H-z)^{n+1}].
$$
Here $A$ is the <ice> rate factor, distinct from the cross-sectional <area> in the river problem. Integrating this <velocity profile> through the thickness gives the <volume flux> per unit valley width:
$$
Q=\frac{AG^n}{n+1}\left[H^{n+2}-\frac{H^{n+2}}{n+2}\right]=\boxed{A(\rho g\sin\alpha)^n(1-\cot\alpha H_x)^n\frac{H^{n+2}}{n+2}.}
$$
The factor $H^{n+2}$ combines the depth-dependent <shear stress>, integration to obtain <velocity>, and integration to obtain <flux>. If reverse shear is admitted for noninteger $n$, the signed version of <Glen's flow law> is $u_z=A|\tau|^{n-1}\tau$; the displayed unsigned <power> presumes the downstream regime.
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