web3js – How to Read Data from Smart Contract Using web3.js?

After adding an event like SquareComputed (see How to get values returned by non constant transaction functions?) and web3.js Contract Events example

var event = myContractInstance.MyEvent({valueA: 23} [, additionalFilterObject])

// watch for changes
event.watch(function(error, result){
  if (!error)
    console.log(result);
});

this would lead to code like:

var event = myContractInstance.SquareComputed({});

// watch for changes
event.watch(function(error, result){
  if (!error)
    resolve({
        primary_address: config.ethConfig.primary_address,
        numSquare : result  // need to access the properties of result to obtain the actual square 
    })
  event.stopWatching();
});

Do the above before myContractInstance.squareNumber.sendTransaction. The resolve({numSquare:...}) in the original code should be moved to inside the watch as above.

Other web3.js APIs such as web3.eth.filter can also be used (see How do I retrieve the Voted events from The DAO).

This questions asks "how exactly do I structure my web3js code, to get the value returned (10*10) from the solidity function squareNumber()", otherwise for an overview see What is the difference between a transaction and a call?.

You don't need to do this all by yourself. You can instead use getData method.

const contract = new web3.eth.Contract(contractABI, contractAddress);
const callData = contract.functionName.getData(functionParameters);
const result = web3.eth.call({
    to: "0x692a70d2e424a56d2c6c27aa97d1a86395877b3a", 
    data: callData
});

web3.eth.call executes the call in VM of the node but this is not mined. This is kind of dry run. If you instead want to send a transaction to blockchain use web3.eth.sendTransaction.