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JavaScript (ES7), 60 bytes

a=>[...a].map((v,i)=>eval(v+('+*-/%'[i%6]||'**')+a.pop())|0)

let f =

a=>[...a].map((v,i)=>eval(v+('+*-/%'[i%6]||'**')+a.pop())|0)

console.log(JSON.stringify(f([1, 2, 3, 4, 5, 6, 7, 8, 9]    ))) // [10, 16, -4, 0, 0, 1296, 10, 16, 8]
console.log(JSON.stringify(f([5, 3, 6, 1, 1]                ))) // [6, 3, 0, 0, 1]
console.log(JSON.stringify(f([2, 1, 8]                      ))) // [10, 1, 6]
console.log(JSON.stringify(f([11, 4, -17, 15, 2, 361, 5, 28]))) // [39, 20, -378, 7, 2, 3.32948887119979e-44, 9, 308]