Assign the value to the "text input" cell by the number of clicks on the "button" cell.

I can only figure out how to do this with some JS.

You can use an Application Parameter or and var in the JS. Here is how to do it with the app.param

• Create an application parameter in this case 'myValue'
• Drag the link handle thing from that parameter to the "Text" handle of your textArea
• 
• Then in the buttons add a call to the JS function we are going to create
• 
• Now the JS code

$scope.bump = function () {
 $scope.app.params.myValue = parseInt($scope.app.params.myValue) + 1;
 //you need parseInt as parameters are strings
}