Nice job! I admit, though, that it seems a bit complicated to me. Here's a rough cut of a simpler version.

#!/usr/bin/perl
use strict;
use warnings;

my %operator = (
    '+' => sub { my $i = 0; $i += $_ for @_; $i; },
    '-' => sub { my $i = shift @_; @_ or return -$i; $i -= $_ for @_; 
+$i; },
    '*' => sub { my $i = 1; $i *= $_ for @_; $i; },
    '/' => sub { my $i = shift @_; @_ or return 1/$i; $i /= $_ for @_;
+ $i; },
);

my $ops = join '' => keys %operator;
my $task = "( + 3 4 ( * 2 7  ( + 1 1 ) ) ( / 6 2 ) )";
1 while $task =~ s/\(\s*([$ops])((?:\s*\d+)+)\s*\)/
    local $_ = $2;
    $operator{$1}->(split);
/e;
print $task;
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