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Is there anyway to loft 4 edges into a smooth surface?

I have this smooth structure I am modeling and it has 4 sides, the top is a 3D spline and there is a curved face at the front and a straight edge on the bottom, and I want the it to end in a radius at the end, is there any way to form these into a smooth surface? I have been able to make it into a surface but not a smooth one following the profile I want it to take. Any help would be much appreciated.
This is the current state of what I am trying to create, you cant see it in this picture really but the top edge is a spline, you can sort of see the opposite side and that's the profile of the spline.
Answers
Can you post a link to your document?