I tested seven free online Binomial Probability Calculators on a difficult test case
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     >> Note: "sealevel.info" is mine, but I tried to be fair and impartial <<

Test case (a real-world problem, as it happens):
n=35750,  k=20,  p=1/9999 (or 0.0001000100010001 if entering a rational value for "p" isn't supported)

                       Supports
NAME                   "1/9999"?   P(X = 20)                          ∑P(X ≤ 20)                        ∑P(X > 20)
---------------------  --------    --------------------------         --------------------------        --------------------------

sealevel.info ("slow")    Y        1.336562893500049e-9               0.9999999997288647                2.711353770861858e-10
(p=0.0001000100010001)    *        1.336562893500046e-9               0.9999999997288647                2.711353770861854e-10
("quick")                 Y        1.3365628935e-9                    0.99999999973                     2.7e-10

Casio Keisan (22 digits)  Y        1.33656289350004855552E-9          0.9999999997288646229138          2.711353770861858284764E-10 (set k=21 to calc)
(p=0.0001000100010001)    *        1.336562893500046360045E-9         0.9999999997288646229138          2.71135377086185350827E-10 (set k=21 to calc)
(30 digits)               Y        1.3365628935000485555210338634E-9  0.999999999728864622913814171524  2.71135377086185828476351193568E-10 (set k=21 to calc)

WolframAlpha              Y        1.337e-9                           1 - 2.711e-10 (set k=21 to calc)  2.711e-10
                                                                      (which is 0.9999999997289)

Harvey Berman             N*       0                                  1                                 0

VassarStats               Y        <0.000001                          >.999999                          <0.000001

iCalcu                    N*       1.336562893519394e-9               0.9999999997424598                n/a
                                   (last 5 digits are wrong)          (last 5 digits are wrong)

Richard Lowrey            Y        "Sorry. Your value of n is too large."


* means p=0.0001000100010001 instead of p=1/9999

All tests were run on March 1, 2024.

Conclusions:
1. Casio Keisan is best.
2. My sealevel.info is second best.
3. WolframAlpha is third best.

Dave Burton  3/1/2024
sealevel.info