RPN really excels when chaining calculations, and in fact promotes thinking like this instead of setting up formal expressions to be evaluated left to right. For example, you want to drive a small LED at 2mA, so you have a simple BJT: 12V supply, a resistor, the LED, and a BJT - and you just want a ballpark figure for Ib so you can size a resistor for it to interface to a 3.3V CMOS output.
So you start with the supply voltage 12V.
Subtract Vce(sat) for the transistor, say 0.25V.
Subtract Vf for the LED. Now you're left with the voltage over R.
Hmm, maybe we should also check the power dissipation of R?
So DUP it on the stack.
Divide the voltage on the stack by R, now we have Ic.
Calculate the power dissipation: dup, over, *, swap; now we have it in Y and Ic in X
Approximate Ie = Ic, and divide by min current gain for the BJT
Now we need the base resistor voltage: 3.3V, subtract 0.65 for Vbe
Divide this by the current in Y: swap, divide
Now we have the base resistor resistance in X, and the current limiting resistor dissipation in Y
As a result of doing this, you will have implicitly sanity checked every single step of the way.
No pen and paper needed to sit and write up expressions to type in on the calculator. In addition to the transcription stage you only get very limited partial results out of algebraic calculators.