This is a often nearly "normal" problem with more than one reason.

As first the poser render engine is optimized for curvy figures, like human or other beings. So it tries to bend all things in somewhat natural manner. In nature normally no sharp edges or really plan sides are seen.
So you get every time most difficulties trying to do straight things, e.g. buildings.

As second 4 point polygons works better than 3 point polygons. As worst as possible are narrow polygons. Multi point polygons will fail completely as I remember.

There are 2 known solutions:
Don't weld vertices at sharp edges. For example with the cylinder have three separat pieces for the top and bottom circle and the outside hull. UV mapper function split vertices.
Poser stops bending the polygons at such sharp edges. Along this edge having vertices doubled is no problem.

Other solution if split isn't usable have a second line parallel to the edge line with only a small difference.  Poser seems to use a spline function for it's bending. If having to lines nearby there isn't room enough to to have a big bend and as the bend spline is used for all connected polygons that small bend will effect to the complete area.

Though it might also be a matter of wrong normals in this case it seem not to be. The shaded parts are to regular and I can't see anything like transparence what is the fact with wrong normals.
Also if you look to the middle of the outside hull the shadows will center. I guess that hull consists of 2 polygon circles, one top polygon and one bottom polygon, right ? So we have also a small bending influence.

Quote - I tried unchecking the smooth polygons in the parameter dials. No work.

As far as smoothing is touched. The checkmark smoothing on/off and the value for smoothing angle in parameter pallet belongs together, for sure.
But they are used independently. In my test I have found that unchecking smoothing doesn't do anything to that problem if used alone. The value is used further on.
Try smooth angle 5, 10 or 20 and than uncheck the mark.
This should work lot's better but without the both solution above it will not solve that shadowing completely. Not on a really sharp edged figure. It might work best if smoothing is too much but no sharp line is needed.