To get this in MoI, right now you'll need to extrude the curve into a surface, and then trim using that extruded surface.

Here's an example sequence to follow to cut a sphere into 2 pieces that are solid.

Draw a sphere in the top view.

Draw a curve in the front view that bisects the sphere into 2 pieces.

Select the curve, and Extrude it, make the extruded surface larger than the sphere, the "Both sides" option in extrude can be convenient here.

Now you don't need the curve anymore, you can delete it.

Select both the sphere and the extruded surface, and do a Trim.

At the "Select cutting objects" prompt in Trim, just push Done. This tells MoI that the pieces that are being cut are also cutting objects to each other, a "mutual trimming" operation.

Now there is the option to remove different pieces. Just push Done here to cut everything and leave all the pieces behind. (You can right click in a viewport to be the same thing as Done, by the way).

Now you have all the pieces that you can use to assemble your solid cut sphere pieces.

Select the outside portion of the extruded surface and delete it.

Select one part of the sphere and hide it.

Select the interior part of the extruded surface and do Edit/Copy (we need to duplicate it later to attach it to the other part of the sphere).

Now select the extruded surface and the visible sphere half and do a join. This has created one of the solid sphere halves. Move this piece off to the side.

Push "Hide" again to show the other sphere half, do a paste to get the duplicated inner extruded part, and then join those 2 parts together, now you have the second solid sphere portion.

Let me know if anything here isn't clear or isn't what you wanted.

Eventually I would like to automate this and make it an option built into Trim or the booleans, it will probably be a little while before I'll be able to work on that, though.

- Michael