Why is the anode (+) in a device that consumes power & (-) in one that provides power? I was trying to figure out the flow of electrons in a battery connected to a circuit. Conventionally, current is from the (+) terminal to the (-) terminal of the battery. Realistically it flows the other way round; from the (-) terminal to the (+) terminal. My question is, assuming electron flow is from the (-) terminal, would the battery's cathode be located at the (+) terminal and it's anode at the (-) terminal or would it be vice versa?
Another question: Why would the anode be positive in a device that consumes power and negative in a device that provides power?
 A: Electric current is the rate of flow of electric charges across any cross-sectional area of a conductor. The direction of electric current is taken as the direction of flow of positive ions or opposite to the direction of flow of free electrons. Your assumption is not necessary here... Electrons always flow from negative terminal to positive terminal.
$$i=\frac{dq}{dt}$$
When current flows through an electrolytic solution or during the process of electrolysis, The plate towards which positive ions (cations) flow is called the cathode and the plate towards which negative ions (anions) flow is called the anode.
Wikipedia says clearly,

In an electrochemical cell, The electrode at which electrons leave the cell and oxidation occurs is called anode and the electrode at which electrons enter the cell and reduction occurs is called cathode. Each electrode may become either the anode or the cathode depending on the direction of current through the cell. A bipolar electrode is an electrode that functions as the anode of one cell and the cathode of another cell.

So, the convention is totally based on our definition of  the direction of current flow that it always flows opposite to the direction of electrons (i.e) electrons can be called as cations or anions depending on the usage. And based on this, we dump our thought that cathode should always be negative, etc...
