How to deform one side precisely? I want to precisely (it's important) deform one side of the object to follow some kind of curve (in this particular case - an arc, part of a regular circle). This manual modification (I pulled edges one by one), I hope, explains what I want:

I tried to move top edges with proportional editing but it also affects bottom side (it just bends the whole object). Probably, there is a way to lock bottom faces or detach it from modification temporarely.

Finally, it should be a bar with flat bottom and very gentle slope (two slopes actually), forming an radial arc from the side view and it must have exact height in the middle. Some kind of bridge or overpass, just solid. It would be nice to make other forms of slopes (straight slopes for instance) the same way. Thanks in advance!
Using H  to hide, and Alt + H  to unhide you can effectively mask off parts you don't want proportionally edited.

I don't personally know a more precise way but hopefully someone posts one.