下記のようなJavaScriptのコードでAPIにPOSTのリクエストを送信すると、Internal Server Errorが返ってきてしまいます。

追記：OSはUbuntuでwebサーバーはApache、ブラウザはFirefoxを使っています。

apitest.html

<!DOCTYPE html>
<html>
<head>
  <meta charset="utf-8" />
  <title>WolftamAlphaAPItest</title>
  <script src="https://code.jquery.com/jquery-3.2.1.min.js"></script>
</head>
<body>
  <table id="table" border="1">
    <tr><th>Alternate Form</th></tr>
  </table>

  <script>
    var rbFileName = '';
    rbFileName = 'http://xxxxxxxxxxxxxxxxxxxx/wapi.rb';

    var results;

    var querymml = '<math><mrow%20class="integration-node"><mi%20class="character-node">a</mi><mi%20class="character-node">%2B</mi><mi%20class="character-node">b</mi><mi%20class="character-node">=</mi><mi%20class="character-node">2</mi><msqrt%20class="structure-node"><mrow%20class="integration-node%20highlight"><mi%20class="character-node">a</mi><mi%20class="character-node">b</mi></mrow></msqrt></mrow></math>';
    $.ajax({
            type: 'POST',
            url: rbFileName,
            async: false,
            traditional: true,
            dataType: "json",
            data: {query: querymml},            
            success: function(json) {
                results = json;
                console.log(json);
                showResult( results );
            },
            error: function(XMLHttpRequest, textStatus, errorThrown) {
                alert(
                    'XMLHttpRequest : ' + XMLHttpRequest.status + '\n' +
                    'textStatus : ' + textStatus + '\n' +
                    'errorThrown : ' + errorThrown.message
                );
            },
      });
    function showResult( result ) {

        $("#table").append("<tr><td>" + result + "</td><td>");

    }
  </script>
</body>
</html>

wapi.rb

#!/usr/bin/ruby

require 'cgi'
require 'net/http'
require 'json'
require 'uri'

cgi = new CGI.new()

mml = cgi['query']

input = "input=#{mml}"

INPUT = "#{input}"
APPID = 'appid=XXXXXXXXXXXXXXXX'
INCLUDEPODID = 'includepodid=Alternate form'
FORMAT = 'format=mathml'

uri = "http://api.wolframalpha.com/v2/query?" + 
        "#{APPID}&#{INPUT}&#{INCLUDEPODID}&#{FORMAT}"

uri = URI.parse(uri)
req = Net::HTTP::Get.new(uri)
res = Net::HTTP.start(uri.host, uri.port){|http|
    http.request(req)
}

data = {result: res}

cgi.out ({ "type" => "application/json", "charset" => "UTF-8" }) {
    data.to_json
}

error.log

[Sun Jul 21 06:25:01.796620 2019] [mpm_prefork:notice] [pid 32227] AH00163: Apache/2.4.18 (Ubuntu) configured -- resuming normal operations
[Sun Jul 21 06:25:01.796646 2019] [core:notice] [pid 32227] AH00094: Command line: '/usr/sbin/apache2'
[Sun Jul 21 11:34:32.637240 2019] [cgid:error] [pid 30236] (13)Permission denied: AH01241: exec of '/xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx/wapi.rb' failed
[Sun Jul 21 11:34:32.637484 2019] [cgid:error] [pid 29278] [client 180.9.169.100:52500] End of script output before headers: wapi.rb, referer: http://xxxxxxxxxxxxxxxxxxxxxxxxxx/wolframApi.html