Why can't I return stdout variable in this exec function?

Because you return from the function before the exec is finished and the callback is executed.

Exec in this case is asynchronous and unfortunately there is no synchronous exec in node.js in the last version (0.10.x).

There are two ways to do what you are trying to do.

Wait until the exec is done

var exec = require('child_process').exec,

function callPythonFile (args, callback) {
  var out = null
  exec("../Prácticas/python/Taylor.py 'sin(w)' -10 10 0 10", 
    function (error, stdout, stderr) {
      if (error !== null) 
        callback(err);
      callback(null, out);
    });
}

//then you call the function like this:

callPythonFile(args , function (err, out) {
  console.log('output is', out);
});

You will see this pattern a lot in node.js, instead of returning something you have to pass a callback.

Return a ChildProcess object

The exec function returns a ChildProcess object which is basically an EventEmitter and has two important properties stdout and stderr:

var exec = require('child_process').exec,

function callPythonFile (args) {
  return exec("../Prácticas/python/Taylor.py 'sin(w)' -10 10 0 10");
}

//then you call the function like this:

var proc = callPythonFile(args)
proc.stdout.on('data', function (data) {
  //do something with data
});

proc.on('error', function (err) {
  //handle the error
});

The interesting thing is that stdout and stderr are streams, so you can basically pipe to files, http responses, etc. and there are plenty of modules to handle streams. This is an http server that always call the process and reply with the stdout of the process:

var http = require('http');

http.createServer(function (req, res) {

  callPythonFile(args).stdout.pipe(res);

}).listen(8080);