This confuses me every single time:
In Simpson's rule, my teacher has a bit of a mnemonic to remember it, which is: First + last, 4 x odd and 2 x even.
What would the 'odd' and 'even' be referring to? Like, if you had a table of values, is it whether the x value is an odd/even number? Or is it if you count across from the first and last values, every second one is odd, and the others are even?
Any clarification would be super helpful! 
\,dx\\ \text{with 11 function values. Then, we would have this:})
\begin{align*} f(3) &\to \text{first}\\ f(3.2) &\to \text{odd}\\ f(3.4) &\to \text{even}\\ f(3.6)&\to \text{odd}\\ f(3.8 ) &\to \text{even}\\ f(4) &\to \text{odd}\\ f(4.2) &\to \text{even}\\ f(4.4) &\to \text{odd}\\ f(4.6) &\to \text{even}\\ f(4.8 )&\to \text{odd}\\ f(5)&\to \text{last} \end{align*}
That "mnemonic" is a very well known way of memorising the generalised Simpson's rule. Essentially your "first" input value is \(x_0 = 3\). The next input value, \(x_1 = 3.2\), is called "odd" in this context because the index is \(1\). The subsequent input value, \(x_2 = 3.4\), is called "even" in this context because the index is \(2\). And so on.
Essentially, you start counting
after the "first". That one, will be the first "odd".
You should always end up with exactly one more "odd" than "even"
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