WP 34S on DM 42 integral fail

[Albert Chan]

XCas> gaussquad(surd(x,-3), x,-2.,3.)

0.739024156625

This work ! But, I would advice split the integral yourself, to be safe.
Adaptive scheme may be fooled. (no matter how good it is, it only see sample points)

Below is adaptive simpson's scheme to do above integral.
Note line 150. It never touched undefined point at x=0
(But, if integral limits changed, say, -2 .. 6, it will hit x=0 dead on)

10 X1=-2 @ X3=3 @ E=.0001
20 T=TIME @ X2=(X3+X1)/2 @ CALL F(X1,F1) @ CALL F(X2,F2) @ CALL F(X3,F3)
30 S=(F1+4*F2+F3)*(X3-X1)/6
40 CALL SIMPSON(X1,X2,X3,F1,F2,F3,32*E,S) @ DISP S,TIME-T @ END
50 SUB F(X,Y) @ Y=SGN(X)*ABS(X)^(-1/3) @ STOP

100 SUB SIMPSON(X1,X3,X5,F1,F3,F5,E,S)
110 H=(X5-X1)/4 @ X2=X1+H @ X4=X5-H
120 CALL F(X2,F2) @ CALL F(X4,F4)
130 H=H/3 @ S1=(F1+4*F2+F3)*H @ S2=(F3+4*F4+F5)*H
140 S3=S1+S2 @ D=S3-S @ H=E/2
150 IF H<1.E-15 OR ABS(D)<H THEN S=S3+D/15 @ STOP
160 CALL SIMPSON(X1,X2,X3,F1,F2,F3,H,S1)
170 CALL SIMPSON(X3,X4,X5,F3,F4,F5,H,S2)
180 S=S1+S2

>RUN
 .73902427614      18.76

Update: slightly modified SIMPSON() recurse condition, with following:

40 CALL SIMPSON(X1,X2,X3,F1,F2,F3,30*E,S) @ DISP S,TIME-T @ END
150 IF H<15E-15 OR ABS(D)<H THEN S=S3+D/15 @ STOP

> RUN
 .73902420507      15.44

The changes is to compare Sharp BASIC translated HP71B code speed.