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You need more lambdas! When you're doing numerical stuff you usually want to work with Python functions rather than symbolic expressions, like so:

plot((lambda k: find_root(lambda x: F(x, k) - 1/2, 0, 100)), (k, 1, 10))

This ensures that x and k are numbers when you write F(x,k), so it will evaluate to a number (as desired).