How do I Build a structure with a curved side and a cubed side

I’m trying to model a structure that has vertical walls, is rounded in the front and square in the back. (Imagine the floor plan as a face-down tombstone - or rather a mitten, as it will have a door passage in one side.) It must be hollow. I tried mashing a cube and a cylinder together (Right shape, but I couldn’t subdivide the top of the cylinder to hollow it out), building the curved front from a NURB curve (Made a sail-shaped thing but couldn’t control the location of the corner points), and building the whole thing from a cube and rounding out the front end (Looks great, but couldn’t trim the corners without getting unwanted trim along other axes as well).

Does anyone have any suggestions about which would be the best way to start modeling this structure? Thanks!

Here’s a quick doodle showing how the structure should be shaped:

Try this method.
Create a circle

Extrude it

Delete on side

Extrude the edges twice. one time long, then short and join them together.

Then select all and extrude them on Z axis to get this.
Now go ahead a model your design.