did you try beveling the edges?
select or shift select the edges you want too look smoother, > Edit Polygon > bevel > choose a distance and how many segments you want to aadd into the edge, maybe go with t a 3 segment and estimate the distance (undo if not right distance) till you get it right where you want. try rendering it and see if it works.
9 months into Maya...and still learning...
0 experience with any other 3D programs