One way (*edited):
using ImplicitEquations, Plots; gr()
f1(x) = x + 6; f1(x,y) = f1(x)
f2(x) = x^3; f2(x,y) = f2(x)
f3(x) = -x/2; f3(x,y) = f3(x)
f4(x,y) = y
plot((f4 ≦ f1) & (f4 ≧ f2) & (f4 ≧ f3), ylims=(-10,10), fc=:blues, widen=false) # \leqq[tab], \geqq[tab]
plot!(f1, -5, 5, c=:black)
plot!(f2, c=:black)
plot!(f3, c=:black)
