Split string and apply function on string parts

With the sample text in A1
This regular formula seems to calculate the correct values:

=IFERROR(SUMPRODUCT((INDEX(--TRIM(MID(SUBSTITUTE("+"&A1,"+",REPT(" ",LEN(A1))),LEN(A1)
*ROW(INDIRECT("1:"&LEN(A1)-LEN(SUBSTITUTE(A1,"+",""))+1)),LEN(A1))),0)^2)/(4*PI())),0)

EDITED TO INCLUDE THIS ALTERNATIVE:
This seems to work fine, also

=IFERROR(SUMPRODUCT(((0&TRIM(MID(SUBSTITUTE(A1,"+",REPT(" ",100)),(ROW(INDIRECT("1:"&(LEN(A1)
-LEN(SUBSTITUTE(A1,"+",""))+1)))-1)*100+1,100)))^2)/(4*PI())),0)

Is that something you can work with?