Shipping rates estimator calculator

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Does anyone know the code changes to make the shipping rates calculator pictured at the top of the instrucitons found here:

when coded as per instrucitons into a sectioned theme? The end result I get is simply a single return saying rates from... and then one rate shows. I would like the call to return all available rates. Please advise. I am aware that apps can do this, but do not see the cost benefit of having one. I currently have the Shopify code turned off while I trial an App in the hopes I can get the Shopify code to return all available rates for a given area.