R[n_,l_,r_] := Sqrt[(2/(n a))^3 (n-l-1)!/(2 n ((n+l)!)^3)] Exp[-r / (n a) ](2 r / (n a))^l LaguerreL[n-l-1, 2 l+1, (2 r/(n a))]

Y[l_,m_,θ_, ϕ_] := SphericalHarmonicY[l,m,θ,ϕ]

Ψ[n_,l_,m_, r_, θ_,ϕ_] := R[n,l,r] Y[l,m,θ, ϕ]

Integrate[Conjugate[Ψ[1,0,0, r, θ,ϕ] ]r Ψ[1,0,0,r, θ, ϕ] r^2 Sin[θ], {r,0, Infinity}, {θ, 0, Pi}, {ϕ, 0, 2 Pi}, Assumptions->a>0.0]

4 Pi *Integrate[R[3,0,r]r R[3,0,r] r^2 , {r,0, Infinity},Assumptions->a0>0.0]

Integrate[Conjugate[Y[1,0,θ,ϕ]] Y[1,0,θ,ϕ] Sin[θ], {θ,0,Pi}, {ϕ,0, 2 Pi}]

Integrate[ Sin[θ],  {θ, 0, Pi}, {ϕ, 0, 2 Pi}]