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The following is only a workaround, and it likely extremely slow.

sage: f(y) = integrate(x^x,x,1,y)
sage: plot(lambda y: f(y), (y,2,10))

You can see that it's slow because even

sage: plot(lambda y: f(y), (y,2,10),plot_points=10,adaptive_recursion=2)

is really slow.

If you give up on symbolic stuff, though, then

sage: plot(lambda y: numerical_integral(x^x,1,y)[0],(y,2,10))

is a good substitute. Notice that we probably still will need the lambda solution, or to define a Python function.