I have a numerical procedure that reads data from a file and builds a composition of maps from the half-plane to the slit half-plane.  Maple does not deal with this very well symbolically.  I want to use the complex values from this function as a vector field and plot some integral curves.  The 'mystery' function below is a stand-in for the real thing*

I can get DEplot to at least show the vector field, but it fails mysteriously on drawing any curves,...

I have a command in Maple that looks like