sub integrate(&@)
{
    local $x;
    my $sum;
    my $f = shift;
    my %o = (from => 0, by => 0.01, @_);
    for ($o{from} / $o{by} .. $o{to} / $o{by}) {
        $x = $_ * $o{by};
        $sum += &$f * $o{by};
    }
    $sum;
}

#> integrate { $x } from => 0, to => 1
## 0.505
[download]

sub integrate(&@)
{
    my $f = shift;
    ## Set up some sensical defaults for ranges and vars:
    my ($from, $to, $by, $vars) = do {
        my %o = @_;
        for (qw(from to by vars)) {
            $o{$_} = [$o{$_}] if exists $o{$_} && ! ref $o{$_};
        }
        my $dim = @{$o{from}};
        $o{vars} = [qw(x y z w)[0..$dim-1]] unless $o{vars};
        $o{from} = [(0) x $dim] unless $o{from};
        $o{by} = [(0.01) x $dim] unless $o{by};
        @o{qw(from to by vars)};
    };
    my $vol = 1;
    $vol *= $_ for @$by;
    ## Generate nested evaluation loops:
    local *intgen = sub {
        my ($n, $body) = @_;
        if ($n < 0) {
            '$sum += &$f * ' . $vol;
        } else {
            my ($by, $v) = ($by->[$n], $vars->[$n]);
            my ($lo,$hi) = ($from->[$n] / $by, $to->[$n] / $by);
            "for \$$v ($lo .. $hi) { \$$v *= $by ;\n"
                . intgen($n-1)
                . "\n}\n";
        }
    };

    ## Do it:
    (eval 'sub { my $f = shift; my $sum = 0;'.intgen($#{$from}).' $sum
+ }')
        ->($f);
}

#> integrate { $x * $y } from => [0,0], to => [1,1]
## 0.255025
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Indeed an interesting and clean approach!! As minor remark for a side note, when doing numerical integration one may likely be concerned about speed - not that relevant after all: I know full well that "premature optimization is the root of all evil", and if one is really concerned then he'd probably not doing this in Perl at all...

But all those dereferentiations and method accesses do not make for *speed* and apart a clean syntax I'm not really sure about what this gives you more than a C-style for loop which for once seems appropriate! (Most often in my experience it is not.)

Whatever, I stress once again that especially for educational purposes I find it great. In this sense, just for fun here's my rewrite of your code according to my own stylistic preferences. It should be just the same as yours modulo one tiny change in logic ("adaptive delta")

#!/usr/bin/perl

use strict;
use warnings;

package Range;

sub new {
    my ($class, $lower, $upper, $delta) = @_;
    bless {
        lower => $lower,
        upper => $upper,
        delta => $delta || ($upper-$lower)/1000,
        current => $lower,
    }, $class;
}

sub next {
    my $self = shift;
    ($self->{current} += $self->{delta}) < $self->{upper};
}

package main;

sub integrate {
    my ($function, $iter) = @_;
    my $sum;
    $sum += $function->($iter->{current}) * $iter->{delta} while $iter
+->next;
    $sum;
}

printf "%.2f\n", integrate sub {(shift)**2}, new Range (2, 5);

__END__
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