The landscape form factor, in my experience, is less likely to get in the way of my book or paper than a portrait form factor. Probably because we write left to write then top to bottom, and read the same way, and so a landscape form factor overlaps fewer lines than the same area in portrait form factor.
A phone calculator in landscape mode is not as good for a couple reasons. First, phones tend to turn off when idle for a bit. It gets annoying to have to keep unlocking the thing.
Second, without physical buttons it is a lot harder to operate without looking.
This later problem could be addressed if you made a physical overlay that you could put over you phone screen, which covers the key section of the phone calculator, and has a hole over each key. Make the overlay thick enough that it is easy to feel where the holes are. That should provide enough feedback to let you use the calculator without looking.
(Fancier would be to make an overlay that actually has physical buttons. Make the buttons out of something that conducts touch, so that when you press it the button touches the screen).
The third is all the distractions of a modern phone.
The combination of textbook, notepad and pencil, and calculator, is perfect for deep study of a complex topic.
I didn't know this was a common problem.
These days I mostly use PCALC on my iPhone. I like the ability to customize the number displayed lines from 4 up to 8. There's free version too : PCALC Lite
At one point somebody made a metal band that goes across the back of the calculator and holds the batteries in. They don't seem to be available anymore, but that's basically what I need because my battery door is in decent shape, but the case is cracking at the corners.
My desktop calculator these days is an HP-35S which is to find and inexpensive. I've been thinking about a Swiss Micro clone of the HP-15C but it's hard for me to justify the purchase.