Cathy,
In InDesign anything can be a text frame if you click in it with the text tool, so you can use drawn shapes as well as rectangular text frames drawn with the text tool.
One way to make a semi-circular frame would be to use the ellipse shape tool to draw a circle, then use the scissors tool to cut it at two points, and delete the half you don't want. ID will happily fill the path with color or text, or both, stopping along the line joining the two end-points. This won't work well, however, if you need a stroke around the frame because the path is open.
Are you familiar with using the pen tool to draw and modify bezier curves? You can use the pen tool to delete on of the nodes on a circle, but you will be left with rounded corners rather than sharp ones, and a curved side that you can modify using the direct select tool to collapse the direction control handles next to the side you want to be straight.
When using the pen tool it automatically becomes the delete point tool when you hover over an existing point, or the add point tool when you hover over a selected path anywhere else. Holding the Ctrl key with the pen tool active will temporarily change to the direct select tool.
Peter