gistfile1.txt

$ cat intgood
#!./perl6-m

sub leftrect(&f, $a, $b, $n) {
   my $h = ($b - $a) / $n;
#  my $sum = [+] do f($_) for $a, *+$h ... $b-$h;    # gets prior def of &f somehow
   my $sum = [+]   (f($_) for $a, *+$h ... $b-$h);   # works
   $h * $sum;
}
 
sub tryem($f, $a, $b, $n, $exact) {
    say "\n$f\n   in [$a..$b] / $n";
    EVAL "my &f = $f;
	say '              exact result: ', $exact;
	say '     rectangle method left: ', leftrect  &f, $a, $b, $n;"
}
 
tryem '{ $_ ** 3 }', 0, 1, 100, 0.25;
 
tryem '{ 1 / $_ }', 1, 100, 100, log(100);

$ ./intgood

{ $_ ** 3 }
   in [0..1] / 100
              exact result: 0.25
     rectangle method left: 0.245025

{ 1 / $_ }
   in [1..100] / 100
              exact result: 4.60517018598809
     rectangle method left: 5.17098406528658

$ cat intbad
#!./perl6-m

sub leftrect(&f, $a, $b, $n) {
   my $h = ($b - $a) / $n;
   my $sum = [+] do f($_) for $a, *+$h ... $b-$h;    # gets prior def of &f somehow
#  my $sum = [+]   (f($_) for $a, *+$h ... $b-$h);   # works
   $h * $sum;
}
 
sub tryem($f, $a, $b, $n, $exact) {
    say "\n$f\n   in [$a..$b] / $n";
    EVAL "my &f = $f;
	say '              exact result: ', $exact;
	say '     rectangle method left: ', leftrect  &f, $a, $b, $n;"
}
 
tryem '{ $_ ** 3 }', 0, 1, 100, 0.25;
 
tryem '{ 1 / $_ }', 1, 100, 100, log(100);

$ ./intbad

{ $_ ** 3 }
   in [0..1] / 100
              exact result: 0.25
     rectangle method left: 0.245025

{ 1 / $_ }
   in [1..100] / 100
              exact result: 4.60517018598809
     rectangle method left: 2378916309.88410399