Can't define a name for my Angular app when using with RequireJS

I decided to use RequireJS with AngularJS.

<script data-main="/app.js" src="/bower_components/requirejs/require.js"></script>
<div ng-app>
    Hello {{"angular-require_test"}} world!
</div>

This works. But strangely, if I try to name my app (ng-app="app") it breaks

<script data-main="/app.js" src="/bower_components/requirejs/require.js"></script>
<div ng-app="app">
    Hello {{"angular-require_test"}} world!
</div>

It throws the error

Uncaught Error: [$injector:modulerr]     
http://errors.angularjs.org/1.2.23/$injector/modulerr?p0=app&p1=Error%3A%20…90347)%0A%20%20%20%20at%20X%20(http%3A%2F%2Flocalhost%2Fapp.js%3A9%3A90557) app.js:9

Example hosted at runnable. It's the version that works. Add ng-app="app" to the index.html to break it : http://runnable.com/U_46hUAJdhQwnzSP/angular-require_test-for-node-js

Here's the rest of my code/setup:

server.js:

var express = require('express');
var app = express();
app.use(express.static('.'));
app.use('bower_components', express.static('bower_components'));
var server = require('http').createServer(app);
server.listen(80, function() {
    console.info('Express server started');
});

Gruntfile.js:

module.exports = function grunt(grunt) {
    require('load-grunt-tasks')(grunt);
    grunt.initConfig({
        requirejs: {
            compile: {
                options: {
                    baseUrl: '.',
                    mainConfigFile: 'main.js',
                    paths: {
                        jquery: 'bower_components/jquery/dist/jquery.min',
                        angular: 'bower_components/angular/angular.min'
                    },
                    shim: {
                        'angular': {
                            exports: 'angular',
                        },
                    },
                    name: 'main',
                    out: 'app.js',
                }
            }
        },
    });
    grunt.registerTask('default', ['requirejs']);
};

main.js

require(['jquery', 'angular'], function($, angular){
    $(document).ready(function(){
        alert('jquery loaded, document ready');
    });
});