use warnings;
use strict;

# 例 x^2 定積分の近似値
my $a = 0;
my $b = 1;
my $N = 99;
my $Integrand = '$x*$x';
	
my $ThreeEighthsRule = &THREEEIGHTHSRULE($a, $b, $N, $Integrand);
print "$ThreeEighthsRule\n";

# 3/8公式 Three-Eighths Rule
# 引数 左端a 右端b 分割数 被積分関数 ($a, $b, $N, \@Integrand)
# 戻り値 3/8公式 ($ThreeEighthsRule)
sub THREEEIGHTHSRULE{
	my ($a, $b, $N, $Integrand) = @_;
	 ($a, $b) = ($b, $a) if($a > $b);
	my $ThreeEighthsRule = 0;
	my $h = ($b - $a) / $N;
	my $Sum = 0;
	my $SumA = 0;
	my $SumB = 0;

	# 分割数の確認
	if(($N < 3) || (($N % 3) != 0)){
		return 0;
	}
	
	# 計算
	$SumA = &INTEGRAND($a, $Integrand);
	$SumB = &INTEGRAND($b, $Integrand);
	
	for(my $i = 1; $i < $N; $i++){
		my $x = $a + ($i * $h);
		my $num = ($i % 3 == 0 ? 2 : 3);
		my $tmp = &INTEGRAND($x, $Integrand);
	
		$Sum += $num * $tmp;
	}
	
	# 3/8公式 Three-Eighths Rule
	$ThreeEighthsRule = ($SumA + $Sum + $SumB) * $h * (3 / 8);
	
	return $ThreeEighthsRule;
}

# 被積分関数 Integrand
# 引数 積分変数 被積分関数 (\@Integrand)
# 戻り値 被積分関数 ($Integrand)
sub INTEGRAND{
	my ($x, $Integrand) = @_;
	my $tmp = eval($Integrand);

	return $tmp;
}