Only 12 functions? The premise of this poll seems premature. The fundamental question of whether to load the keyboard top row or dedicate them to menu soft keys is still open, is it not?
It seems to me that the question(s) of keybpard loading are fundamental to the operation (or operability) of the calculator. My preference would be to "load" the keyboard. I would propose blue and yellow functions (in addition to the primary functions) for the second row. The top row would be re-assignable soft keys, but absent a menu call these keys would have assigned primary and yellow-shifted functions.
Loading the top row with a primary and shifted function (in addition to the soft key assignment) and adding a second shifted function to the second row would give us 30 spots (or 32, counting USER/ALPHA on the third row) and would cover most of the above list of potential functions. This is the question that should be answered first: load the keyboard, or not? Then, we debate the 18, 24, 30, or 32 most popular functions and their placement.
In case I'm alone in this, here are my 12 functions:
1. 1/x (I'd actually make this a data entry key along with +/-, EEX, and backspace, but surely >almost< all at least agree that it has to be on the keyboard. I'd make this a primary key.)
2. SQRT (This seems fundamental to me, and I'd like it to be primary. However with only 6 keys, I'd make it the yellow-shift of 1/x.)
3-8. SIN, COS, and TAN with shifted ASIN, ACOS, and ATAN.
9-10. LN with shifted e^x.
11. LG
12. y^x as the shifted function of LG. (I'd prefer 10^x be located on the LG key with y^x as a separate, primary key but real estate dictates.)
With the exception of #1, these are primary functions in that no closed-form calculation exists. With these functions and some stack, we can calculate most anything else that's missing, like H.MS, rect/polar, degrees/radians, TVM, parallel, and IP, FP. Some of these will be bigger losses in terms of convenience/usability than others, and this will vary by person. We >can<, however, get to them without menus. Unfortunately (and I see this as a major compromise) complex numbers, probability, and statistics are completely relegated to menus.
-Bill