label set_fn_number   # Call this with the number of the entry label to the function
sto fn_entry_label_int   # Store in a memory address
rtn
label simpson_int   # Simpson's rule integration. Push lower limit, upper limit, and number of points
sto steps_int   # number of steps to perform
sto holdsteps_int   # This value won't be overwritten
x==0
rtn    # don't run if asked to perform zero steps
clx
sto highlimit_int   # The upper limit of the integration
clx
sto lowlimit_int   # The lower limit of the integration
x<>i
sto callers_i_int   # store the calling routine's I register, if any
x<>i
clx
0.000000000000000e+000
sto integral_int   # initialize to zero
clx
rcl highlimit_int
rcl lowlimit_int
-
rcl steps_int
/
2.000000000000000e+000
/
sto stepsize_int   # distance between function invocations
clx
rcl lowlimit_int
sto current_x_int   # make a current x for f(x)
clx
label mainloop_int
rcl fn_entry_label_int
x<>i
clx
rcl current_x_int
gosub (i)   # run the function being integrated
rcl fn_entry_label_int   # in case the function killed I, reload it
x<>i
clx
2.000000000000000e+000
*
sto+ integral_int
clx
rcl stepsize_int
sto+ current_x_int
clx
rcl current_x_int
gosub (i)
rcl fn_entry_label_int   # in case the function killed I, reload it
x<>i
clx
4.000000000000000e+000
*
sto+ integral_int
clx
rcl stepsize_int
sto+ current_x_int
clx
1.000000000000000e+000
sto- steps_int
clx
rcl steps_int
cf notfinished_int
x!=0
sf notfinished_int
clx
f? notfinished_int
goto mainloop_int
rcl lowlimit_int
gosub (i)
rcl fn_entry_label_int   # in case the function killed I, reload it
x<>i
clx
sto- integral_int   # I overdid it in the loop, take one off
clx
rcl highlimit_int
gosub (i)
rcl fn_entry_label_int   # in case the function killed I, reload it
x<>i
clx
sto+ integral_int
clx
rcl highlimit_int
rcl lowlimit_int
-
6.000000000000000e+000
/
rcl holdsteps_int
/
sto* integral_int
clx
rcl integral_int
rcl callers_i_int   # restore the caller's I register
x<>i
clx
rtn
label root_int   # Find a zero of the function based on the guess provided
sto trialx_int
clx
rcl fn_entry_label_int
x<>i
sto callers_i2_int
clx
label mainloop_root_int
rcl trialx_int
sto last_trialx_int
gosub (i)
rcl fn_entry_label_int   # in case the function killed I, reload it
x<>i
clx
rcl trialx_int
gosub deriv_int
/
sto- trialx_int
clx
rcl trialx_int
round
rcl last_trialx_int
round
x==y    # iterate until there's no printable change from last time
goto finished_root_int
clx
clx
goto mainloop_root_int
label finished_root_int
clx
clx
rcl callers_i2_int
x<>i
clx
rcl trialx_int
rtn
label deltasize_int   # delta-x / x to use for differentiating
sto new_delta_int
rtn
label deriv_int   # get the derivative of the function
rcl fn_entry_label_int
x<>i
sto callers_i3_int
clx
rcl new_delta_int
x!=0
goto deriv_setup_int
5.000000000000000e-005 # Default value of delta-x / x
sto new_delta_int
clx
label deriv_setup_int
clx
ENTER
ENTER
ENTER
rcl new_delta_int
*
2.000000000000000e+000
/
+
gosub (i)
rcl fn_entry_label_int   # in case the function killed I, reload it
x<>i
clx
x<>y
ENTER
rcl new_delta_int
*
2.000000000000000e+000
/
-
gosub (i)
rcl fn_entry_label_int   # in case the function killed I, reload it
x<>i
clx
-
rcl new_delta_int
/
x<>y
/
rtn