#import math
# Don't need to import anything yet, but in R the command is library
#def fun(x):
#    return x+math.sin(2**x) # in python need ** instead ^
fun <- function(x){
    x+sin(2^x) # R functions return the last computed thing
    # R has some trig preloaded and is OK with ^
    }
#from scipy.integrate import quad  #R already has integrate preloaded
a <- -1 # <- instead of = 
b <- 2
bubba <- integrate(fun,lower=a,upper=b) # first element is integral estimate, second element is
# an estimate of an upper bound on the error
# intV = quad(fun,a,b)[0]
# errV = quad(fun,a,b)[1]
#print(intV)
print(bubba)
intV <- bubba$value #this is like a data frame with column name 'value'
N <- c(2,4,8,16,32,64) # instead of [2,4,8,16,32,64]
left <- c()
right <- c()
trap <- c()
simp <- c()
#exact = [intV for n in N] # list comprehension does not work easily in R
exact <- c()
for (j in N){
    exact <- c(exact, intV)
    }
#for n in N:
    #h = (b-a)/n
    #x = [a+j*h for j in range(n+1)]
    #y = [fun(bubba) for bubba in x]
    #left += [h*sum(y[:-1])] # y[:-1] means all indices up through the 2nd last index
    ## y[A:B] means indices A through B-1.
    #right += [h*sum(y[1:])]
    #trap += [h/2*(y[0]+y[-1]+2*sum(y[1:-1]))] # note y[1:-1]=y[1:n]
    #simp += [h/3*(y[0]+y[-1]+4*sum(y[1:-1:2])+2*sum(y[2:-1:2]))]
    ##y[1:-1:2] means indices 1,3,5,...,stop before the last #
for (n in N){
    h <- (b-a)/n
    x <- c()
    for (j in 0:n){ # in R, 2:7 means 2 3 4 5 6 7
        x <- c(x,a+j*h)
        }
    y <- c()
    for (xx in x){ 
        y <- c(y,fun(xx))
        }
    }
y