A calculator as a list of numbers and operators

JavaScript (ES6) 53

A function taking an array as input.

Run the snippet in Firefox to test.

f=a=>a.map(t=>t<'0'?o=t:v=eval(v+o+t)|0,v=0,o='+')&&v

// TEST
out=x=>O.innerHTML=x;

input = [5,8,25,"*",9,6,2,"-",104,"/",4,7,"+",6,"%",14];
out(input.join(' ')+' -> '+f(input));

function go() {
  i=I.value.split(/ +/),out(I.value+' -> '+f(i))
}  

<pre id=O></pre>
Your test:<input id=I><button onclick='go()'>GO</button>

Pyth - 24 23 22 20 bytes

2 bytes saved thanks to @issacg and 1 thanks to @orlp!

Uses reduce with base case of 0 and checks for ' being in repr to detect string vs. int.

u.xsv++GbH&=bHG+\+QZ

Does not work online because I use full eval which is disabled online for security reasons. Takes input from stdin in a list as such: 5, 8, 25, "*", 9, 6, 2, "-", 104, "/", 4, 7, "+", 6.

Julia, 85 83 bytes

s->(o=0;p="+";for i=split(s) isdigit(i)?o=eval(parse("ifloor($o$p$i)")):(p=i)end;o)

This creates an unnamed function that accepts a string as input and returns an integer.

Ungolfed:

function f(s::String)
    # Assign the starting output value o and operator p
    o = 0
    p = "+"

    # Split the input string into an array on spaces
    for i = split(s)
        if isdigit(i)
            # Assign o using string interpolation
            o = eval(parse("ifloor($o $p $i)"))
        else
            # Assign p to the new operator
            p = i
        end
    end
end

Fixed issue and saved 2 bytes thanks to Glen O.