HP50 : indefinite integral of '0^x' gives '?' and 0 for '0*x'

[rawi]

This seems to be a strange problem for calculators:
HP Prime: G1 and G2:
Integral 0^x without lower and upper limit in CAS: undef.
Integral from a to b of 0^x --> invalid input (ungültige Eingabe, home) or undef. (CAS)
Integral from 1 to 2 of 0^x --> invalid input (Home) or undef. (CAS)

TI 89 Titanium and TI nspire CX II T CAS:
Integral 0^x without lower and upper limit: no result (input is repeated as result)
Integral from a to b of 0^x --> no result (input is repeated)
Integral from 1 to 2 of 0^x --> 0

I think the reason why the integrals from a to b do not work is that 0^0 is undefined in all the calculators (there seems to be a new definition among mathematicicians but I am not sure about that). But the integral from 1 to 2 should be no problem.