;  /---------------------------------------------------------------------\
;  |                         I n t e g r a t e                           |
;  |                                                                     |
;  |                            for the HP-41                            |
;  \---------------------------------------------------------------------/
;
;                                   1.00
;         https://coertvonk.com/technology/hp41/integrate-4625

01      LBL "IG"	; init by
02      "F-NAME ?"	;   store constants (b-a)/4 in R16
03      AON		;   store constants (b+a)/4 in R17
04      STOP
05      ASTO 10
06      AOFF
07      SF 10
08      STO 17
09      X<>Y
10      -
11      4
12      /
13      STO 16
14      ST- 17
15      ST- 17
16      .		; initialize Sk, k and M(k,k) for k=0
17      STO 15
18      STO 11
19      STO 18
20      SF 09		; for at least two iterations (see 089-090)
21      LBL 01		; calculate u0 and the step size 2^(k-1)
22       E
23      2
24      STO 14
25      RCL 11
26      CHS
27      Y^X
28      ST* 14
29       E
30      -
31      LBL 02
32      STO 12
33      X^2		; calculate xi
34      -
35      STO 13
36      2
37      +
38      RCL 12
39      *
40      RCL 16
41      *
42      RCL 17
43      +
44      XEQ IND 10	; calculate f(xi)
45      RCL 13
46      *
47      ST+ 15		; calculate Sk
48       E
49      RCL 12
50      RCL 14
51      +
52      X<Y?
53      GTO 02
54      RCL 11		; calculate M(k,0)
55      STO 13
56      18
57      STO 12
58       E
59      ST+ 11
60      RCL 15
61      RCL 16
62      1.5
63      *
64      *
65      RCL 14
66      *
67      LBL 03		; calculate M(k,j)
68      R^
69      4
70      *
71      ENTER^
72      DSE Y
73      X<> Z
74      ENTER^
75      X<> IND 12
76      ST- Y
77      RND
78      X<> Z
79      /
80      RCL IND 12
81      +
82      ISG 12
83      STOP
84      DSE 13
85      GTO 03
86      STO IND 12
87      FS? 10
88      VIEW X
89      FS?C 09
90      GTO 01
91      RND		; end when two consecutive rounded approximations
92      X#Y?		;   are equal
93      GTO 01
94      LASTX		; recall the final approximation and halt.
95      RTN
96	END